Intercept

1. Determine the intercepts of the line.

$y$-intercept: ( _____, ______ )

$x$-intercept: ( _____, ______ )

2. Determine the intercepts of the line.

$y$-intercept: ( _____, ______ )

$x$-intercept: ( _____, ______ )

3. Determine the intercepts of the line.

$y$-intercept: ( _____, ______ )

$x$-intercept: ( _____, ______ )

4. Determine the intercepts of the line.

$y$-intercept: ( _____, ______ )

$x$-intercept: ( _____, ______ )

1.

The $y$-intercept is the point where the graph intersects the $y$-axis. Since the $y$-axis is also the line $x = 0$, the $x$-value of this point will always be $0$.

The $x$-intercept is the point where the graph intersects the $x$-axis. Since the $x$-axis is also the line $y = 0$, the $y$-value of this point will always be $0$.

By looking at the graph, we can see that:

• The $y$-intercept is $(0, 275)$.
• The $x$-intercept is $(125, 0)$.

2.

The $y$-intercept is the point where the graph intersects the $y$-axis. Since the $y$-axis is also the line $x = 0$, the $x$-value of this point will always be $0$.

The $x$-intercept is the point where the graph intersects the $x$-axis. Since the $x$-axis is also the line $y = 0$, the $y$-value of this point will always be $0$.

By looking at the graph, we can see that:

• The $y$-intercept is $(0, 0.4)$.
• The $x$-intercept is $(0.3, 0)$.

3.

The $y$-intercept is the point where the graph intersects the $y$-axis. Since the $y$-axis is also the line $x = 0$, the $x$-value of this point will always be $0$.

The $x$-intercept is the point where the graph intersects the $x$-axis. Since the $x$-axis is also the line $y = 0$, the $y$-value of this point will always be $0$.

By looking at the graph, we can see that:

• The $y$-intercept is $(0, -45)$.
• The $x$-intercept is $(-10, 0)$.

4.

The $y$-intercept is the point where the graph intersects the $y$-axis. Since the $y$-axis is also the line $x = 0$, the $x$-value of this point will always be $0$.

The $x$-intercept is the point where the graph intersects the $x$-axis. Since the $x$-axis is also the line $y = 0$, the $y$-value of this point will always be $0$.

By looking at the graph, we can see that:

• The $x$-intercept is $(-7.5, 0)$.
• The $y$-intercept is $(0, 5.5)$.

1. Determine the intercepts of the line.
Do not round your answers.

$4 x-3 y=17$

$y$-intercept: ( _____, ______ )

$x$-intercept: ( _____, ______ )

2. Determine the intercepts of the line.
Do not round your answers.

$y-3=5(x-2)$

$y$-intercept: ( _____, ______ )

$x$-intercept: ( _____, ______ )

3. Determine the intercepts of the line.
Do not round your answers.

$y=11 x+6$

$x$-intercept: ( _____, ______ )

$y$-intercept: ( _____, ______ )

4. Determine the intercepts of the line.
Do not round your answers.

$-7 x-6 y=-15$

$y$-intercept: ( _____, ______ )

$x$-intercept: ( _____, ______ )

1.

The $y$-intercept is the point where the graph intersects the $y$-axis. Since the $y$-axis is also the line $x = 0$, the $x$-value of this point will always be $0$.

The $x$-intercept is the point where the graph intersects the $x$-axis. Since the $x$-axis is also the line $y = 0$, the $y$-value of this point will always be $0$.

To find the $y$-intercept, let's substitute $x = 0$ into the equation and solve for $y$:

$\begin{aligned} 4 \cdot 0-3 y &=17 \\ -3 y &=17 \\ y &=-\frac{17}{3} \end{aligned}$

So the $y$-intercept is $\left(0,-\frac{17}{3}\right)$.

To find the $x$ intercept, let's substitute $y = 0$ into the equation and solve for $x$:

$\begin{array}{r} 4 x-3 \cdot 0=17 \\ 4 x=17 \\ x=\frac{17}{4} \end{array}$

So the $x$-intercept is $\left(\frac{17}{4}, 0\right)$.

In conclusion,

• The $y$-intercept is $\left(0,-\frac{17}{3}\right)$.
• The $x$-intercept is $\left(\frac{17}{4}, 0\right)$.

2.

The $y$-intercept is the point where the graph intersects the $y$-axis. Since the $y$-axis is also the line $x = 0$, the $x$-value of this point will always be $0$.

The $x$-intercept is the point where the graph intersects the $x$-axis. Since the $x$-axis is also the line $y = 0$, the $y$-value of this point will always be $0$.

To find the $y$-intercept, let's substitute $x = 0$ into the equation and solve for $y$:

$\begin{aligned} y-3 &=5(0-2) \\ y-3 &=-10 \\ y &=-7 \end{aligned}$

So the $y$-intercept is $(0, -7)$.

To find the $x$ intercept, let's substitute $y = 0$ into the equation and solve for $x$:

$\begin{aligned} 0-3 &=5(x-2) \\ -3 &=5 x-10 \\ 7 &=5 x \\ 1.4 &=x \end{aligned}$

So the $x$-intercept is $(1.4, 0)$.

In conclusion,

• The $y$-intercept is $(0, -7)$.
• The $x$-intercept is $(1.4, 0)$.

3.

The $x$-intercept is the point where the graph intersects the $x$-axis. Since the $x$-axis is also the line $y = 0$, the $y$-value of this point will always be $0$.

The $y$-intercept is the point where the graph intersects the $y$-axis. Since the $y$-axis is also the line $x = 0$, the $x$-value of this point will always be $0$.

To find the $x$ intercept, let's substitute $y = 0$ into the equation and solve for $x$:

$\begin{aligned} 0 &=11 x+6 \\ -6 &=11 x \\ -\frac{6}{11} &=x \end{aligned}$

So the $x$-intercept is $\left(-\frac{6}{11}, 0\right)$.

To find the $y$-intercept, let's substitute $x = 0$ into the equation and solve for $y$:

$\begin{aligned} &y=11 \cdot 0+6 \\ &y=6 \end{aligned}$

So the $y$-intercept is $(0, 6)$. Generally, in linear equations of the form $y=m x+b$ (which is called slope-intercept form), the $y$-intercept is $( 0, b)$.

In conclusion,

• The $x$-intercept is $\left(-\frac{6}{11}, 0\right)$.
• The $y$-intercept is $(0, 6)$.

4.

The $y$-intercept is the point where the graph intersects the $y$-axis. Since the $y$-axis is also the line $x = 0$, the $x$-value of this point will always be $0$.

The $x$-intercept is the point where the graph intersects the $x$-axis. Since the $x$-axis is also the line $y = 0$, the $y$-value of this point will always be $0$.

To find the $y$-intercept, let's substitute $x = 0$ into the equation and solve for $y$:

$\begin{aligned} -7 \cdot 0-6 y &=-15 \\ -6 y &=-15 \\ y &=\frac{15}{6} \\ y &=\frac{5}{2} \end{aligned}$

So the $y$-intercept is $\left(0, \frac{5}{2}\right)$.

To find the $x$ intercept, let's substitute $y = 0$ into the equation and solve for $x$:

$\begin{aligned} -7 x-6 \cdot 0 &=-15 \\ -7 x &=-15 \\ x &=\frac{15}{7} \end{aligned}$

So the $x$-intercept is $\left(\frac{15}{7}, 0\right)$.

In conclusion,

• The $y$-intercept is $\left(0, \frac{5}{2}\right)$.
• The $x$-intercept is $\left(\frac{15}{7}, 0\right)$.

1. This table gives a few $(x,y)$ pairs of a line in the coordinate plane.

What is the $x$-intercept of the line?

2. This table gives a few $(x,y)$ pairs of a line in the coordinate plane.

What is the $y$-intercept of the line?

3. This table gives a few $(x,y)$ pairs of a line in the coordinate plane.

What is the $x$-intercept of the line?

4. This table gives a few $(x,y)$ pairs of a line in the coordinate plane.

What is the $y$-intercept of the line?

1.

An $x$-intercept is a point on the line that is on the $x$-axis, which is a point where the $y$-value is $0$.

For points on a line, a constant change in the $x$-value brings a constant change in the $y$-value. Let's use this fact to find the point where the $y$-value is $0$.

The table shows that for each increase of $19$ in $x$, there's a decrease of $11$ in $y$.

Let's start at $(33,-22)$ and extend the table backwards to get to a $y$-value of $0$:

In conclusion, the line's $x$-intercept is $(-5,0)$.

To verify, here is the graph of the line. You can see it passes through all the points we've seen, including the $x$-intercept at $(-5, 0)$.

2.

A $y$-intercept is a point on the line that is on the $y$-axis, which is a point where the $x$-value is $0$.

For points on a line, a constant change in the $x$-value brings a constant change in the $y$-value. Let's use this fact to find the point where the $x$-value is $0$.

The table shows that for each increase of $7$ in $x$, there's an increase of $14$ in $y$.

Let's start at $(-14,-26)$ and extend the table to get to an $x$-value of $0$:

In conclusion, the line's $y$-intercept is $(0,2)$.

To verify, here is the graph of the line. You can see it passes through all the points we've seen, including the $y$-intercept at $(0,2)$.

3.

An $x$-intercept is a point on the line that is on the $x$-axis, which is a point where the $y$-value is $0$.

For points on a line, a constant change in the $x$-value brings a constant change in the $y$-value. Let's use this fact to find the point where the $y$-value is $0$.

The table shows that for each increase of $15$ in $x$, there's a decrease of $10$ in $y$.

Let's start at $(-8,20)$and extend the table to get to a $y$-value of $0$:

In conclusion, the line's $x$-intercept is $(22,0)$.

To verify, here is the graph of the line. You can see it passes through all the points we've seen, including the $x$-intercept at $(22, 0)$.

4.

A $y$-intercept is a point on the line that is on the $y$-axis, which is a point where the $x$-value is $0$.

For points on a line, a constant change in the $x$-value brings a constant change in the $y$-value. Let's use this fact to find the point where the $x$-value is $0$.

The table shows that for each increase of $16$ in $x$, there's an increase of $5$ in $y$.

Let's start at $(32,22)$and extend the table backwards to get to an $x$-value of $0$:

In conclusion, the line's $y$-intercept is $(0,32)$.