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Find the equation of the line that is parallel to the line y=-3x and passes through the point (-2,-9) . Write the equation in slope-intercept form.

User Chinmoy Panda
by
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1 Answer

25 votes
25 votes

Answer:

y=-3x-15

Explanation:

Hi there!

We want to find the equation of the line that is parallel to the line y=-3x and passes through the point (-2, -9).

We want that line written in slope-intercept form, which is y=mx+b, where m is the slope and b is the y intercept

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

In the equation y=-3x, -3 is taking the place of where m is. So -3 is the slope of y=-3x

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

So we can substitute -3 as m in y=mx+b. Hence,

y=-3x+b

Now we need to find b

As the equation passes through (-2, -9), we can use it to solve for b

Substitute -2 as x and -9 as y into the equation

-9=-3(-2)+b

Multiply

-9=6+b

Subtract 6 from both sides

-15=b

Substitute that value as b into the equation

y=-3x-15

Hope this helps!

User Sean Dunford
by
2.7k points