Question

Which choices are equations for the line shown below? Check all that apply.

(-2, 4)
(1-2)

Answer 1

A, C and F.

Explanation:

Equation of a line:

The equation of a line has two formats:

`y = mx + b`

Slope-intercept format, in which m is the slope and b is the y-intercept(which is the value of x when y = 0).

And in point-slope form:

`y - y(0) = m(x - x(0))`

In which (x(0),y(0)) is the point and m is the slope.

Slope:

When we have two points on a line, the slope is given by the change in y divided by the change in x. We have points (-2,4), (1,-2). So

Change in y: -2 - 4 = -6

Change in x: 1 - (-2) = 1 + 2 = 3. So

m = -6/3 = -2.

Equation in slope-intercept:

The y-intercept is y = 0, so b = 0. The equation in slope-intercept formula is:

`y = -2x`, so option A is marked.

Equation if point-slope:

Point (-2,4) means that
`x_0 = -2, y_0 = 4`. So

`y - y(0) = m(x - x(0))`

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

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

So option C is correct.

Point (1,-2) means that
`x_0 = 1, y_0 = -2`. So

`y - y_0 = m(x - x(0))`

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

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

So option F is correct.

Answer:

Options A, C and F are correct.