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Sagot :
Given that the line passes through the points (-2,0) and (2, -4)
Slope of the line:
The slope m of the line is calculated as
[tex]\begin{gathered} m\text{ = }\frac{\text{rise}}{run}=\frac{y_2-y_1}{x_2-x_1} \\ \text{where } \\ y_1=0 \\ x_1=-2 \\ y_2=-4 \\ x_2=2 \end{gathered}[/tex]Thus,
[tex]m=\frac{-4-0}{2-(-2)}=-\frac{4}{4}=-1[/tex]Thus, the slope of the line is -1
The equation of the line:
The equation of a line passing through two points is given as
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ \text{where m=}\frac{y_2-y_1}{x_2-x_1} \end{gathered}[/tex]Thus, we have
[tex]\begin{gathered} y-0=-1(x-(-2)) \\ y=-1(x+2) \\ y=-x-2 \end{gathered}[/tex]Thus, the equation of the line is y= -x-2
The line intersects the y-axis at (0,2):
The point at which the line intersects the y-axis is the intercept. At the intercept, the value of x equals zero.
Thus, the corresponding value of y when x equals zero will be
[tex]y=-x-2=-0-2=-2[/tex]Thus, the line intersects the y-axis at (0,2)
The line intersects the x-axis at (-2,0):
When the line intersects the x-axis, the value of y equals zero. Thus, the corresponding value of x when y equals zero will be
[tex]\begin{gathered} y=-x-2 \\ 0=-x-2 \\ \text{collecting like terms, we have} \\ 0+2=-x \\ x=-2 \end{gathered}[/tex]Thus, the line intersects the x-axis at (-2,0)
Hence, options A, B, C, and D are true.
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