Question #171a8

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Answer 1 · 2017-03-16T07:58:39

$y = x + 17$ $y = x+17" "$

Lines which are parallel have the same slope.
Change the given equation into the form $y = m x + b$ $y = color(red)(m)x+b$

$4 y - 4 x = 8 \to 4 y = 4 x + 8 \to y = 1 x + 2$ $4y -4x =8" "rarr 4y = 4x +8" "rarry = color(red)(1)x+2$

Now we can see the slope. $m = 1$ $color(red)(m = 1)$

The new line has $m = 1$ $color(red)(m = 1)$ and passes through $(- 7, 10)$ $(color(blue)(-7),color(magenta)(10))$

You can use the formula $y - y_{1} = m (x - x_{1})$ $y-color(magenta)(y_1) =color(red)(m)(x-color(blue)(x_1))$

$y - (10) = 1 (x - (- 7)) \leftarrow$ $y -(color(magenta)(10)) = color(red)(1)(x-(color(blue)(-7)))" "larr$ now simplify

$y - 10 = x + 7$ $y-10 = x+7$

$y = x + 7 + 10$ $y = x+7+10$

$y = x + 17$ $y = x+17" "$ is the equation of the new line.