Question #7903f

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Answer 1 · 2017-10-27T17:40:17

$y = - \frac{2}{3} x - 2$ $y=-2/3x-2$

If it is parallel the gradients will be the same for both lines.
To find the gradient of the equation given it needs to be rearranged in to the form:

$y = m x + c$ $y=mx+c$

this gives us:

$3 y = 3 - 2 x$ $3y=3-2x$ then divide by 3 to cancel $3 y$ $3y$ to $y$ $y$
$= y = - \frac{2}{3} x + 1$ $=y=-2/3x+1$

gradient = $m$ $m$ , therefore gradient is equal to $- \frac{2}{3}$ $-2/3$

now we know the gradient and a point on the line we can substitute these values in the $y = m x + c$ $y=mx+c$ to find the value of $c$ $c$

this gives us:
$- 4 = - \frac{2}{3} (3) = c$ $-4=-2/3(3)=c$

when solved for $c$ $c$ we get $c = - 2$ $c=-2$

with the gradient value and the value of $c$ $c$ the equation is:
$y = - \frac{2}{3} x - 2$ $y=-2/3x-2$