Find the equation of a line that is parallel to the line y = 4x and contains the point (4, -6).

Question

Find the equation of a line that is parallel to the line y = 4x and contains the point (4, -6).

Answer 1

Hello, Yasmine,

The line y = 4x has a slope of 4 and an intercept of zero (there is no "b" in the standard equation y = mx + b). The slope (m = 4) will be the same slope as any parallel line. Parallel lines will all have the same slope.

So let's go back to the standard format and change the m to a "4."

y = 4x + b

Now let's use the point that lies on this line and put the values into the equation and solve for "b."

-6 = 4(4) + b

-6 - 16 = b

b = -22

The equation of this parallel line is y = 4x - 22

I hope this helps,

Bob

Answer 2

First, consider the equation of a line: y=ax+b

Recall: if two lines are parallel, their slopes are equal.

We want to find a line that is parallel to line y=4x, that means the slope of the line that we want to find is 4.

Rewrite the equation of line: y = 4x+b

Since this line contains(4, -6), we can solve for b. Plug the point into y=4x+b, -6=4(4)+b, b=-22

Hence, the equation for the line is y=4x-22

Answer 3

This question requires the point-slope equation:

y-y₁ = m(x-x₁)

(x₁, y₁) represents the coordinate of a point and m represents a slope.

The given line is y = 4x, which is a linear line that passes through the origin and has a slope of 4. A parallel line will have the same the slope as the given line. Thus the slope used for m in the calculation is also 4.

Gather the information:

slope, m = 4

point (4,-6)

Now input these values into their respective positions of the point-slope form from above.

y-y₁ = m(x-x₁)

y-(-6) = 4(x-4)

Simplify:

y+6 = 4x-16

y = 4x-22