Graphing Slope-Intercept Equations

1. Graph $y=-x-6$.

2. Graph $y=\frac{2}{3} x-4$

3.Graph $y=-3 x+7$.

4. Graph $y=\frac{6}{5} x+1$.

1. The equation is in slope-intercept form: $y=m \cdot x+b$. In this form, $m$ gives us the slope of the line and $b$ gives us its $y$-intercept.

So $y=-x-6$ has a slope of $-1$ and a $y$-intercept at $(0,-6)$.

We need two points. We already have the $y$-intercept $(0,-6)$.

We can find a second point by reasoning about the slope. A slope of $-1$ means when the $x$-value increases by $1$, the $y$-value decreases by $1$.

$(0+1,-6-1)=(1,-7)$

Now we can graph the equation.

2. The equation is in slope-intercept form: $y=m \cdot x+b$. In this form, $m$ gives us the slope of the line and $b$ gives us its $y$-intercept.

So $y=\frac{2}{3} x-4$ has a slope of $\frac {2}{3}$ and a $y$-intercept of $(0. -4)$.

We need two points. We already have the $y$-intercept $(0,-4)$.

$(0+3,-4+2)=(3,-2)$

Now we can graph the equation.

3. The equation is in slope-intercept form: $y=m \cdot x+b$. In this form, $m$ gives us the slope of the line and $b$ gives us its $y$-intercept.

So $y = -3x+7$ has a slope of $-3$ and a $y$-intercept at $(0,7)$.

We need two points. We already have the $y$-intercept $(0,7)$.

We can find a second point by reasoning about the slope. A slope of $-3$ means that when the $x$-value increases by $1$, the $y$-value decreases by $3$.

$(0+1,7-3)=(1,4)$

Now we can graph the equation.

4. The equation is in slope-intercept form: $y=m \cdot x+b$. In this form, $m$ gives us the slope of the line and $b$ gives us its $y$-intercept.

So $y=\frac{6}{5} x+1$ has a slope of $\frac{6}{5}$ and a $y$-intercept at $(1, 0)$.

We need two points. We already have the $y$-intercept $(0,1)$.

We can find a second point by reasoning about the slope. A slope of $\frac {6}{5}$ means that when the $x$-value increases by $5$, the $y$-value increases by $6$.

$(0+5,1+6)=(5,7)$

Now we can graph the equation.