Answer:
Line m: y = -2x + 4
Line p: x = -4
Line l: y = 4
Explanation:
For line m, the 1st step is to determine the slope of the line at (0, 4) and (2, 0) where x1 = 0, y1 = 4, x2 = 2, and y2 = 0.
Solving for the slope(m), we'll have;
[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{0-4}{2-0}=\frac{-4}{2}=-2[/tex]Also, the line m cuts the y-axis at y = 4, therefore the y-intercept(b) of the line is 4.
Given below the general slope-intercept form of the equation of a line;
[tex]y=mx+b[/tex]where m = slope of the line and b = y-intercept of the line
If we substitute the above values for m and b for line m, the equation of the line m can be written as;
[tex]y=-2x+4[/tex]For line p,
Since line p is a vertical line, the slope is undefined and the equation of the line will be the x-intercept of the line;
[tex]x=-4[/tex]For line l,
Since the line is a horizontal line, the slope will be zero and the equation of the line will be the y-intercept of the line;
[tex]y=4[/tex]