A line is parallel to y=4x+11 and intersects the point (-2,4). What is the equation of this parallel line?

Answer 1

To find any line, you need its slope and its y-intercept. These are what define the line.

- Remark that the equation y = 4x + 11 is not your line, it's another line that has a relationship with your line. -

SLOPE

> In this case, this other line is parallel to yours. Which means that they have the same slope (go in the same direction). The slope of the given line is 4 (the # in front of x), so your slope is also 4.

Y-INTERCEPT

> To find the y-intercept you can either:

- Use point-slope form with the given ordered pair (-2, 4) and the slope 4 (using this method gives you the equation)

- Or plug in (-2, 4) as x and y, and 4 as m in the model "y = mx + b" and solving for b, which is the y-intercept.

- Let's use the second model.

y = mx + b

4 = 4(-2) + b

4 = -8 + b

+ 8 on both sides

12 = b

Thus, m = 4 and b = 12

- The equation of your line is y = 4x + 12

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Answer 2

Use point-slope form:

(y - y₁) = m(x - x₁)

(y - 4) = 4(x + 2)