Find the Line Equation: Parallel to -4+y=5x-6 Through (-2,-13)

Choose the function for a straight line that passes through the point (−2,−13) (-2,-13) and is parallel to the line −4+y=5x−6 -4+y=5x-6 .

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:11 Let's find the algebraic form of the function.
00:14 First, we'll isolate Y. Here's how to do it.
00:24 This is the equation of our parallel function.
00:27 And this represents the slope of that parallel function.
00:31 Remember, parallel functions always have the same slopes.
00:35 Next, we'll use the line equation. Let's get started.
00:39 We'll substitute the given point into the equation based on the data.
00:48 Then, substitute the slope, and solve to find the intersection point, B.
01:01 Let's isolate B, the intersection point, in this step.
01:10 This point is where it intersects the Y-axis.
01:18 Now, plug the intersection point and slope back into the line equation.
01:29 And there you go, that's our solution!

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Choose the function for a straight line that passes through the point (−2,−13) (-2,-13) and is parallel to the line −4+y=5x−6 -4+y=5x-6 .

2

Step-by-step solution

First, write out the line equations:

−4+y=5x−6 -4+y=5x-6

y=5x+4−6 y=5x+4-6

y=5x−2 y=5x-2

From here we can determine the slope:

m=5 m=5

We'll use the formula:

y=mx+b y=mx+b

We'll use the point (−2,−13) (-2,-13) :

−13=5×−2+b -13=5\times-2+b

−13=−10+b -13=-10+b

−3=b -3=b

Finally, substitute our data back into the formula:

y=5x+(−3) y=5x+(-3)

y=5x−3 y=5x-3

3

Final Answer

y=5x−3 y=5x-3

Practice Quiz

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Look at the function shown in the figure.

When is the function positive?

xy-4-7

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