Question 1198188
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Plug in y = 0 and solve for x to locate the x intercept.


y = 2x-10
0 = 2x-10
2x = 10
x = 10/2
x = 5
The x intercept is located at (5,0)
This is the location of point A.


Now plug in x = 0 to find the y intercept for the other linear equation
y = -2x+4
y = -2(0)+4
y = 4
The y intercept is (0,4) which is where point B is located.


We want to find the equation of the line through A(5,0) and B(0,4)
We need the slope
{{{m = slope = rise/run = matrix(1,3,"change","in","y")/matrix(1,3,"change","in","x")}}}


{{{m = (y[2] - y[1])/(x[2] - x[1])}}}


{{{m = (4 - 0)/(0 - 5)}}}


{{{m = (4)/(-5)}}}


{{{m = -4/5}}}
We know the y intercept since this line goes through B(0,4)
The y intercept always occurs when x = 0.


We have m = -4/5 as our slope and b = 4 as the y intercept.


Therefore, the slope-intercept equation {{{y = mx+b}}} becomes {{{y = -expr(4/5)x+4}}} which is the final answer.
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