Question 117249
There exists an equation to the line: y=-5/4x+7 that goes through the x-intercept of the line: -3x-17y=9. What is the equation in slope-intercept form?
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Find the x intercept of the equation -3x-17y=9

To find x intercept let y equal 0 and solve for x.

-3x-17(0)=9

-3x -0=9

-3x =9

Divide both sides by -3 to find x.

{{{-3x/-3 = 9/-3}}}

x=-3
(-3,0) is the x intercept.

Given the first equation of a line, find its slope.

y=-5/4x+7

y=mx+b

so, m=-5/4

Now, use point slope form to write the equation for the line with slope of -5/4, passing through (-3,0)---->(x1,y1).

(y-y1) =m(x-x1)

y-0 = -5/4(x-(-3))

y=-5/4(x+3)

{{{y=-5x/4-15/4}}}

Hope that helps.

Regards,
misscrt