Question

Write an equation in slope-intercept form of a line passingthrough the given point and parallel to the given line.3. (-3, -1);2y- 3x= 8

Answer 1

It's required to find the equation of a line that passes through (-3, -1) and is parallel to the line 2y - 3x = 8.

Solving for y:

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

The slope of this line is 3/2 and the required line must have the same slope because they are parallel.

The point-slope form of a line passing through the point (h, k) and slope m is:

y = m(x - h) + k

Substituting:

$\begin{gathered} y=\frac{3}{2}(x+3)-1 \\ Operate. \\ y=\frac{3}{2}x+\frac{9}{2}-1 \end{gathered}$

Simplifying, the required line is:

$y=\frac{3}{2}x+\frac{7}{2}$