Question

Identify an equation in point-slope form for the line parallel to y = 1/2x - 7 thatpasses through (-3,-2).

Answer 1

D.

`y+2=(1)/(2)(x+3)`

Step-by-step explanation:

Given:

`y=(1)/(2)x-7`

Recall that the slope-intercept form of the equation of a line is generally given as;

`y=mx+b`

where;

m = slope of the line

b = y-intercept of the line

Comparing both equations above, we can see that the slope(m) of the line is 1/2 and the y-intercept(b) is -7

Recall that parallel lines have the same slope. So the line that is parallel to the given line will have the same slope(m) of 1/2

Given the point (-3, -2), we can go ahead and write the equation of the parallel line in point-slope form as seen below;

`\begin{gathered} y-y_1=m(x-x_1) \\ y-(-2)=(1)/(2)[(x-(-3)] \\ y+2=(1)/(2)(x+3) \end{gathered}`