Need help ASAP! Parallel line problem!

Question

I’m still very new to the topic, but can anyone help me out? My question is what’s the equation of a line that passed through the point (-2,3) and is parallel to the line whose equation is y=3/2x-4?

Answer 1

Hi Dat B.

Parallel lines have the same slope. Since the line you need to be parallel to has a slope of (3/2) (the number multiplied to the "x"), then your line must also have a slope of (3/2).

Since it needs to pass through (-2,3), we need to write an equation of the form y = mx + b

where m is the slope (3/2) and b is where it crosses the y-axis, known as the "y-intercept".

Since we have a point where x = -2 and y = 3; and we have the slope, we can plug all of these into

the linear equation y=mx+b and solve for b.

y = m x + b

3 = (3/2)(-2) + b

3 = -3 + b

6 = b

Now we can write the equation, filling in just the m and the b and leaving x and y as x and y.

y = (3/2) x + 6

This is the equation of the line you are looking for.