Answer:
Correct options are A and D.
Step-by-step explanation:
From the given graph it is clear that the spaceship is located at (-4,3). The alien is at (-2, -3).
If a line passes through two points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex], then the equation of line is
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]
The equation of line is
[tex]y-3=\frac{-3-3}{-2-(-4)}(x-(-4))[/tex]
[tex]y-3=\frac{-6}{2}(x+4)[/tex]
[tex]y-3=-3(x+4)[/tex]
[tex]y-3=-3x-12[/tex]
Add 3 on both sides.
[tex]y=-3x-12+3[/tex]
[tex]y=-3x-9[/tex] .... (1)
Slope intercept form of a line is
[tex]y=mx+b[/tex] .... (2)
where, m is slope and b is y-intercept.
On comparing (1) and (2) we get
[tex]m=-3,b=-9[/tex]
It means,
Slope = -3
y-intercept = -9
Points from -6 to 6 are labeled on y-axis. The y-intercept is -9, so it is not visible on the graph. Option A is correct.
Substitute y=0 in equation (1) to find the x-intercept.
[tex]0=-3x-9[/tex]
[tex]3x=-9[/tex]
Divide both sides by 3.
[tex]x=-3[/tex]
x-intercept is -3. It means the line crosses the x-axis at -3. Option D is correct.
