Question

Write the equation of a line that is parallel to y=-3/2x -1 and that through the point (4,6)

Answer 1

Answer:

$y=-\frac{3}{2}x+12$

Step-by-step explanation:

Hi there!

We want to write the equation of a line parallel to y=$-\frac{3}{2}x-1$ and that passes through the point (4,6)

Parallel lines have the same slopes, but different y intercepts.

The slope of the equation $y=-\frac{3}{2}x-1$ is $-\frac{3}{2}$, since the equation is written in y=mx+b format (m is slope and b is y intercept), and $-\frac{3}{2}$ is in the place where m is.

It's also the slope of the line parallel to it.

So we know the slope of the new line, let's write it down:

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

Let's find b, in order to complete the equation

Since the equation passes through the point (4, 6), we can use it to solve for b.

Substitute 4 as x and 6 as y into the equation:

6=$-\frac{3}{2}$(4)+b

Multiply

6=-6+b

Add 6 to both sides

12=b

Substitute 12 as b in the equation.

y=$-\frac{3}{2}x+12$

Hope this helps!