Question

Which of the following equations describes the line shown below? Check all
that apply.

Answer 1

B. y = 2x - 2

E.
`y + 4 = 2(x + 1)`

F.
`y - 6 = 2(x - 4)`

Explanation:

The equation of the line can be found using either the point-slope equation or the slope-intercept equation.

✔️Equation of the line in point-slope using the slope and the coordinates of the point (4, 6):

Slope = m = change in y/change in x

Using (4, 6) and (-1, -4),

m = (-4 - 6)/(-1 - 4)

m = -10/-5

m = 2

Substitute m = 2, and (a, b) = (4, 6) into the point-slope equation form
`y - b = m(x - a)`

Thus:

`y - 6 = 2(x - 4)`

✔️Equation of the line in point-slope using the slope and the coordinates of the point (-1, -4):

Slope = m = 2

Substitute m = 2, and (a, b) = (-1, -4) into the point-slope equation form
`y - b = m(x - a)`

Thus:

`y - (-4) = 2(x - (-1))`

`y + 4 = 2(x + 1)`

✔️Equation of the line in slope-intercept form, y = mx + b

Where,

m = slope = 2

b = y-intercept = -2 (the point where the line intercepts the y-axis)

Thus, substitute m = 2 and b = -2 into y = mx + b

y = 2x + (-2)

y = 2x - 2