Question

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

what is the equation of line? write in the form y=mx+b
it passes through (2,-5) and its x-intercept is 4.

Answer 1

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

`= ( - 5 - 0)/(2 - 4) \\ = ( - 5)/( - 2) \\ = (5)/(2)`

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

`0 = ( (5)/(2) )(4) + b \\ 10 + b = 0 \\ b = 0 - 10 \\ = - 10`

therefore equation of line will be:

`y = (5)/(2) x - 10`