Answer:
A, C and F.
Step-by-step explanation:
Equation of a line:
The equation of a line has two formats:
[tex]y = mx + b[/tex]
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:
[tex]y - y(0) = m(x - x(0))[/tex]
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:
[tex]y = -2x[/tex], so option A is marked.
Equation if point-slope:
Point (-2,4) means that [tex]x_0 = -2, y_0 = 4[/tex]. So
[tex]y - y(0) = m(x - x(0))[/tex]
[tex]y - 4 = -2(x - (-2))[/tex]
[tex]y - 4 = -2(x + 2)[/tex]
So option C is correct.
Point (1,-2) means that [tex]x_0 = 1, y_0 = -2[/tex]. So
[tex]y - y_0 = m(x - x(0))[/tex]
[tex]y - (-2) = -2(x - 1)[/tex]
[tex]y + 2 = -2(x - 1)[/tex]
So option F is correct.
Answer:
Options A, C and F are correct.
