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

Sagot :

amysun2025

Answer:

[tex]y=-\frac{3}{2}x+12[/tex]

Step-by-step explanation:

Hi there!

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

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

The slope of the equation [tex]y=-\frac{3}{2}x-1[/tex] is [tex]-\frac{3}{2}[/tex], since the equation is written in y=mx+b format (m is slope and b is y intercept), and [tex]-\frac{3}{2}[/tex] 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=[tex]-\frac{3}{2}x[/tex]+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=[tex]-\frac{3}{2}[/tex](4)+b

Multiply

6=-6+b

Add 6 to both sides

12=b

Substitute 12 as b in the equation.

y=[tex]-\frac{3}{2}x+12[/tex]

Hope this helps!

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