Graphing Slope-Intercept Equations

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.