Question

32. Select the equation that is correctly displayed in point-slope form:

Answer 1

Answer:

$y=-\frac{1}{4}x-\frac{5}{2}$

Step-by-step explanation:

Point-Slope Form: $(y-y_{0})=m(x-x_{0})$ where $(x_{0},y_{0})$ is the point our line is passing through and $m$ is the slope of our line.

The question asks us for an equation parallel to $y=-\frac{1}{4}x+5$.

We identify that the equation provided is in y-intercept form: $y=mx+b$

A line parallel to $y=-\frac{1}{4}x+5$ will have the same slope.

Thus, $m=-\frac{1}{4}$.

We were provided the point $(2,-3)$.

Plugging into our equation for point-slope form:

$(y+3)=-\frac{1}{4} (x-2)$

This is our answer, however we can simplify this equation into y-intercept form by simply solving for y:

$y=-\frac{1}{4}x+\frac{2}{4}-3$

$y=-\frac{1}{4}x+\frac{1}{2}-\frac{6}{2}$

$y=-\frac{1}{4}x-\frac{5}{2}$

Thus, the equation parallel to $y=-\frac{1}{4}x+5$ passing through $(2,-3)$ is:

$y=-\frac{1}{4}x-\frac{5}{2}$