Write an equation of the line with the same slope as the line given by 5x+2y=8 and as the same y-intercept as 3x-7y=10

The slope of the first equation would be -5/2 because

2y=-5x+8

y=-5x/2+4

The y intercept of the 2nd equation is when x=0, so -7y=10

y=-10/7

The equation of the line would be y=-5x/2-10/7

Or in standard form.

5x/2+y=-10/7

5x+27=-20/7

\( 5x+2y=8\ \ \Rightarrow\ \ 2y=-5x+8\ \ \Rightarrow\ \l_1:\ y=- \frac{5}{2}x+8\\ \\ l_2:\ y=ax+b\ \ \ and\ \ \ l_2\ ||\ l_1\ \ \ \Leftrightarrow\ \ \ a=- \frac{5}{2} \\ \\l_2:\ y=- \frac{5}{2}x+b\\ \\3x-7y=10\ \ \ and\ \ \ x=0 \ \ \ \Rightarrow\ \ \ 3\cdot0-7y=10 \ \ \Rightarrow\ \ \ y=- \frac{10}{7} \\ \\b=- \frac{10}{7}\ \ \ \Rightarrow\ \ \ l_2:\ y=- \frac{5}{2}x- \frac{10}{7}\\ \\ l_2:\ \frac{5}{2}x+y=- \frac{10}{7}\ \ /\cdot14\\ \\l_2:\ 35x+7y=-20 \)

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