Question

consider the following equation.y=4/7x-1 What is the equation of the line that passes through the point (-8,-6)and us parallel to the given line . Make the answer in slope intercept form and simplify the answer

Answer 1

The new line is parallel to the given line and therefore will have the same gradiient

Hence the gradient of the new line is 4/7 too

using

$\begin{gathered} y-y_1=\text{ m}(x-x_{1)} \\ \text{where m is the gradient} \end{gathered}$

In this case m = 4/7 and (x1,y1) = (-8,-6)

so substituting for x1 and y1 in the above equation

$\begin{gathered} y\text{ - (-6) = 4/7(x -(-8))} \\ \end{gathered}$

y +6 =4/7 (x +8)

y + 6 = 4/7x + (4/7 x8)

y + 6 = 4/7x + 32/7

y= 4/7x +32/7 -6

$y\text{ = }\frac{4}{7}x\text{ -1}\frac{3}{7}$

simplifying further

$7y\text{ =4x -10}$