Question

I need help with my homework, and the question is:

Answer 1

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

$= \frac{ - 5 - 0}{2 - 4} \\ = \frac{ - 5}{ - 2} \\ = \frac{5}{2}$

Now substitute x = 4, y = 0 and m = 5/2 into equation of line to find b.

$0 = ( \frac{5}{2} )(4) + b \\ 10 + b = 0 \\ b = 0 - 10 \\ = - 10$

therefore equation of line will be:

$y = \frac{5}{2} x - 10$