Answer:
[tex]3x-5y=-20[/tex]
Step-by-step explanation:
We can write the equation of a line in 3 different forms including slope intercept, point-slope, and standard depending on the information we have. We have two standard form equations which we will get a slope and a y-intercept from. We will convert each to slope intercept form to get the information. We will then write a new slope-intercept equation and convert to standard form.
3x-5y=7 has the same slope as the line. Let's convert.
[tex]3x-5y=7\\3x-3x-5y=7-3x\\-5y=7-3x\\\frac{-5y}{-5}=\frac{7-3x}{-5} \\[/tex]
[tex]y=\frac{3}{5}x -\frac{7}{5}[/tex]
The slope is [tex]m=\frac{3}{5}[/tex].
2y-9x=8 has the same y-intercept as the line. Let's convert.
[tex]2y-9x=8\\2y-9x+9x=8+9x\\2y=8+9x\\\frac{2y}{2}=\frac{8+9x}{2}[/tex]
[tex]y=\frac{8}{2}+\frac{9x}{2} \\y=4+\frac{9}{2}x[/tex]
The y-intercept is 4.
We take [tex]m=\frac{3}{5}[/tex] and b=4 and substitute into y=mx+b.
[tex]y=\frac{3}{5}x+4[/tex]
We now convert to standard form.
[tex]-\frac{3}{5}x+y=\frac{3}{5}x-\frac{3}{5}x+4\\-\frac{3}{5}x+y=4[/tex]
For standard form we need the coefficients of x and y to be not zero or fractions. We need integers but the coefficient of x cannot be negative. So we multiply the entire equation by -5 to clear the denominators.
[tex]-5(-\frac{3}{5}x+y=4)\\3x-5y=-20[/tex]
