Write an equation of the line with the same slope as the line given by [tex]5x + 2y = 8[/tex] and the same y-intercept as [tex]3x - 7y = 10[/tex].
Answer (3)
5 x + 2 y = 8 ⇒ 2 y = − 5 x + 8 ⇒ \l 1 : y = − 2 5 x + 8 l 2 : y = a x + b an d l 2 ∣∣ l 1 ⇔ a = − 2 5 l 2 : y = − 2 5 x + b 3 x − 7 y = 10 an d x = 0 ⇒ 3 ⋅ 0 − 7 y = 10 ⇒ y = − 7 10 b = − 7 10 ⇒ l 2 : y = − 2 5 x − 7 10 l 2 : 2 5 x + y = − 7 10 / ⋅ 14 l 2 : 35 x + 7 y = − 20
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
The equation of the line with the same slope as 5 x + 2 y = 8 and the same y-intercept as 3 x − 7 y = 10 is y = − 2 5 x − 7 10 , or in standard form, 35 x + 14 y + 20 = 0 .
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