Answer:
When the line intercepts the x axis, this means that y will be 0.
therefore the 2 coordinates the line passes through are (2,-5) and (4,0)
given equation of line:
y=mx+b
where m = slope
b = y-intercept.
Let (2,-5) and (4,0) be (x1,y1) and (x2,y2) correspondingly.
slope of line = y1-y2 / x1 - x2
[tex] = \frac{ - 5 - 0}{2 - 4} \\ = \frac{ - 5}{ - 2} \\ = \frac{5}{2} [/tex]
Now substitute x = 4, y = 0 and m = 5/2 into equation of line to find b.
[tex]0 = ( \frac{5}{2} )(4) + b \\ 10 + b = 0 \\ b = 0 - 10 \\ = - 10[/tex]
therefore equation of line will be:
[tex]y = \frac{5}{2} x - 10[/tex]
