Question

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

Answer 1

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

Answer 2

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