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Sagot :
We are given the two points (-2, 0) and (2, -4)
We want to check the option(s) that is(are) correct as also given
Solution
Before we start considering the option, Let us find the slope and the equation of the line
The formula for finding slope (m) is given as
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]From the two points given
[tex]\begin{gathered} x_1=-2 \\ y_1=0 \\ x_2=2 \\ y_2=-4 \end{gathered}[/tex]The slope (m) is
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ m=\frac{-4-0}{2-(-2)} \\ m=\frac{-4}{2+2} \\ m=\frac{-4}{4} \\ m=-1 \end{gathered}[/tex]Obviously, Option A is False
Let us find the equation of the line
The formula to use is
[tex]y-y_1=m(x-x_1)[/tex]We now input the parameters
[tex]\begin{gathered} y-y_1=m(x-x_1)_{} \\ y-0=-1(x-(-2)) \\ y=-(x+2) \\ y=-x-2 \end{gathered}[/tex]From here, One can see that Option B is True
Let us check for Option B now
To find the y-intercept
We put x = 0 in the equation we derived
From
[tex]\begin{gathered} y=-x-2 \\ \text{put x = 0} \\ y=-0-2 \\ y=-2 \end{gathered}[/tex]y-intercept is (0, -2)
Therefore, Option B is correct
We are left with option D
Indeed, (-2, 0) is part of the points given already
One can easily conclude that the line intersect the x-axis at (-2, 0)
Hence, Option D is True
The correct Option are B, C and D
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