Question

3. Try It #3 Write the point-slope form of an equation of a line with a slope of -2 that passes through the point (-2,2). Then rewrite it in the slope-intercept form.

Answer 1

Answer:

Point-slope form of equation given as $y-2=-2(x+2)$.

Slope-intercept form of equation is given as $y=-2 x-2$.

Step-by-step explanation:

In the question, it is given that the slope of a line is -2 and it passes from (-2,2).

It is asked to write the point-slope form of the equation and rewrite it as slope-intercept form.

To do so, first find the values which are given in the question and put it in the formula of point-slope form. Simplify the equation to rewrite as slope-intercept form.

Step 1 of 2

Passing point of the line is (-2,2).

Hence, $x_{1}=-2$ and

$y_{1}=2 \text {. }$

Also, the slope of the line is -2.

Hence, m=-2

Substitute the above values in point-slope form of equation given by $y-y_{1}=m\left(x-x_{1}\right)$

$\begin{aligned}&y-y_{1}=m\left(x-x_{1}\right) \\&y-2=-2(x-(-2) \\&y-2=-2(x+2)\end{aligned}$

Hence, point-slope form of equation given as y-2=-2(x+2).

Step 2 of 2

Solve y-2=-2(x+2) to write it as slope-intercept form given by y=mx+c.

$\begin{aligned}&y-2=-2(x+2) \\&y-2=-2 x-4 \\&y=-2 x-4+2 \\&y=-2 x-2\end{aligned}$

Hence, slope-intercept form of equation is given as y=-2x-2.