Question

What is an equation of the line that passes through the point (-2,3) and is parallel to the line whose equation is y=3/2x-4?​

Answer 1

Answer:

Step-by-step explanation:

We can model a line with slope-intercept form:

$y = mx + b$

where $m$ is the slope and $b$ is the Y-intercept.

We know that the new line is parallel to the given line, so the two lines have the same slope, or $m = \frac{3}{2}$:

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

To determine $b$, we just need to plug in the given point that the line passes through, $(-2, 3)$:

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

$(3) = \frac{3}{2}(-2) + b$

$3 = -3 + b$

$b = 6$

This gives us the following equation:

$y = \frac{3}{2}x + 6$