Question

a line passes through the point (-8, -7) and has a slope of 3/2. write an equation in slope-intercept form for this line.

Answer 1

y=(3/2)x+5

Step-by-step explanation:

Given a line with a slope of 3/2 that passes through the point (-8, -7).

To determine the equation of the line, we first use the point-slope form below.

`\begin{gathered} y-y_1=m(x-x_1) \\ m=(3)/(2) \\ (x_1,y_1)=(-8,-7) \end{gathered}`

Substituting, we have:

`\begin{gathered} y-(-7)=(3)/(2)(x-(-8)) \\ y+7=(3)/(2)(x+8) \end{gathered}`

Next, we express the line in the slope-intercept form (y=mx+b).

`\begin{gathered} y+7=(3)/(2)x+12 \\ y=(3)/(2)x+12-7 \\ y=(3)/(2)x+5 \end{gathered}`

The equation of the line in slope-intercept form is:

`y=(3)/(2)x+5`