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

Question

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

00:00 Find the algebraic representation of the function

00:03 Isolate Y

00:13 This is the equation of the parallel function

00:16 This is the slope of the parallel function

00:19 Parallel functions have equal slopes

00:22 We'll use the line equation

00:28 We'll substitute the point according to the given data

00:37 We'll substitute the slope and solve to find the intersection point (B)

00:50 Isolate the intersection point (B)

00:59 This is the intersection point with the Y-axis

01:07 Now we'll substitute the intersection point and slope in the line equation

01:18 And this is the solution to the question

First, write out the line equations:

$-4+y=5x-6$

$y=5x+4-6$

$y=5x-2$

From here we can determine the slope:

$m=5$

We'll use the formula:

$y=mx+b$

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

$-13=5\times-2+b$

$-13=-10+b$

$-3=b$

Finally, substitute our data back into the formula:

$y=5x+(-3)$

$y=5x-3$

$y=5x-3$