Question

Write an equation for the line that passes through the given point and is parallel to the graph of the given equation1. y = 3x - 2 ; (3, 2)2. y = 2/3x + 19 ; (-9, 4) 3. 3x + 4y = 12 ; (-4, 7)

Answer 1

We have an equation of a line and a point and we must find an equation for the line that passes through the given point and is parallel to the graph of the given equation

1.

$y=3x-2\text{ and }(3,2)$

To find the equation we must use the slope of the given equation and the point

$\begin{gathered} m=3 \\ y=3x+b \\ \text{ Replacing the given point} \\ 2=3(3)+b \\ b=2-9=-7 \end{gathered}$

Finally, the equation for the line that passes through the given point and is parallel to the graph of the given equation is

$y=3x-7$

2.

$y=\frac{2}{3}x+19\text{ and }(-9,4)$

To find the equation we must use the slope of the given equation and the point

$\begin{gathered} m=\frac{2}{3} \\ y=\frac{2}{3}x+b \\ 4=\frac{2}{3}(-9)+b \\ b=4+6=10 \end{gathered}$

Finally, the equation for the line that passes through the given point and is parallel to the graph of the given equation is

$y=\frac{2}{3}x+10$

3.

$\begin{gathered} 3x+4y=12\text{ and }(-4,7) \\ \text{ Rewriting the equation} \\ y=-\frac{3}{4}x+3 \end{gathered}$

To find the equation we must use the slope of the given equation and the point

$\begin{gathered} m=-\frac{3}{4} \\ y=-\frac{3}{4}x+b \\ \text{ Replacing the given point} \\ 7=-\frac{3}{4}(-4)+b \\ b=7-3=4 \end{gathered}$

Finally, the equation for the line that passes through the given point and is parallel to the graph of the given equation is

$y=-\frac{3}{4}x+4$