Question

Find the equation of the line passing through the point (2,−4) that is parallel to the line y=3x+2

Answer 1

Hey there! :)

Line passes through (2, -4) & parallel to y = 3x+ 2

Let's start off by identifying what our slope is. In the slope-intercept form y=mx+b, we know that "m" is our slope. "M" is simply a place mat so if we look at our given line, the "m" value is 3. Therefore, our slope is 3.

We should also note that we're looking for a line that's parallel to the given one. This means that our new line has the same slope as our given line. Therefore, our slope for our new line will be 3.

Now, we use point-slope form ( y-y₁=m(x-x₁) ) to complete our task of finding a line that passes through (2, -4) with a slope of 3.

y-y₁=m(x-x₁)

Let's start by plugging in 3 for m (our slope), 2 for x1 and -4 for y1.

y - (-4) = 3(x - 2)

Simplify.

y + 4 = 3x - 6

Simplify by subtracting 4 from both sides.

y = 3x - 10

~Hope I helped!~