Question

Write the equation of the line in slope intercept form that passes through the given point and satisfies the given condition. (-3,-5); parallel to y=-4x+1

Answer 1

Answer:

$y=-4x-17$

Step-by-step explanation:

So we want a line that passes through (-3,-5) and is parallel to y=-4x+1.

Recall that parallel lines have the same slope. This means that our new line must also have a slope of -4.

And with that, we can write our equation by using the point-slope form. The point-slope form is:

$y-y_1=m(x-x_1)$

Let m be -4 and let's let (-3,-5) be x₁ and y₁. Thus:

$y-(-5)=-4(x-(-3))$

Simplify:

$y+5=-4(x+3)$

Distribute the right:

$y+5=-4x-12$

Subtract 5 from both sides:

$y=-4x-17$

And we're done!

Answer 2

Answer:

y = -4x-17

Step-by-step explanation:

y=-4x+1

This is in slope intercept form

y = mx+b where m is the slope and b is the y intercept

The slope is -4

Parallel lines have the same slope

Using the slope intercept form

y = -4x+b

Substituting the point into the equation

-5 = -4(-3) +b

-5 = 12+b

Subtract 12 from each side

-5-12 = b

-17 =b

y = -4x-17