Question

4.(06.02 MC)

The equation of line AB is y = 2x + 4. Write an equation of a line parallel to line AB In slope-Intercept form that contains point (3,-2). (4 points)
O y = 2x + 4
O y = 2x - 8

Answer 1

The equation of a parallel line in the slope-Intercept form that contains the point (3,-2) is:

• y = 2x- 8

Explanation:

The slope-intercept form of the line equation

y = mx+b

where

• m is the slope

• b is the y-intercept

Given the equation of a line

y = 2x + 4

comparing with the slope-intercept form of the line equation

The slope of the line AB is m = 2

We know that the parallel lines have the same slope.

Thus, the slope of the new line is also 2.

now we have,

• The slope of new line m = 2

• The point = (3, -2)

Using the point-slope form of the line equation

`y-y_1=m\left(x-x_1\right)`

where m is the slope of the line and (x₁, y₁) is the point

substituting the values m = 2 and the point (x₁, y₁) = (3, -2)

`y-y_1=m\left(x-x_1\right)`

y - (-2) = 2(x - 3)

y + 2 = 2x - 6

subtracting 2 from both sides

y + 2 - 2 = 2x - 6 - 2

y = 2x- 8

Therefore, the equation of a parallel line in the slope-Intercept form that contains the point (3,-2) is:

• y = 2x- 8