Which choices are equations for the line shown below? Check all that apply.
(-2, 4)
(1-2)

A, C and F.

Step-by-step explanation:

Equation of a line:

The equation of a line has two formats:

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:

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:

, so option A is marked.

Equation if point-slope:

Point (-2,4) means that . So

So option C is correct.

Point (1,-2) means that . So

So option F is correct.

Options A, C and F are correct.

the system of inequalities is

step-by-step explanation:

step 1

find the equation of the dashed line

we have the points

(0,0) and (3,1)

the line passes through the origin, so, is a direct variation

find the slope

the equation of the dashed line is

the solution of the inequality a s the shaded area above the dashed line

therefore

the equation of the inequality a is

step 2

find the equation of the solid line

we have the points

(4,0) and (0,4)

find the slope

the equation of the solid line is

the solution of the inequality b s the shaded area below the solid line

therefore

the equation of the inequality b is

step 3

the system of inequalities is