Question

Passing through (-2,2) and parallel to the line whose equation is 2x-3y=7What is the slope-intercept form?

Answer 1

Given the equation:

2x - 3y = 7

Let's find the equation of a line passing through (-2, 2) which ic parallel to the given line.

Apply the slope-intercept form:

y = mx + b

Where m is the slope and b is the y-intercept.

Rewrite the given equation in slope-intercept form.

• Subtract 2x from both sides:

$\begin{gathered} 2x-2x-3y=-2x+7 \\ \\ -3y=-2x+7 \end{gathered}$

• Divide all terms by -3:

$\begin{gathered} \frac{-3y}{-3}=\frac{-2x}{-3}+\frac{7}{-3} \\ \\ y=\frac{2}{3}x-\frac{7}{3} \end{gathered}$

Therefore, the slope of the given line is 2/3.

Parallel lines have equal slopes.

Hence, the slope of the parallel line will also be 2/3.

Now, we have:

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

Plug in the coordinates of the point (-2, 2) for x and y respectively to find the y-intercept of the parallel line, b.

We have:

$\begin{gathered} 2=\frac{2}{3}(-2)+b \\ \\ 2=\frac{2*(-2)}{3}+b \\ \\ 2=-\frac{4}{3}+b \end{gathered}$

Add 4/3 to both sides:

$\begin{gathered} 2+\frac{4}{3}=-\frac{4}{3}+\frac{4}{3}+b \\ \\ \frac{2(3)+4(1)}{3}=b \\ \\ \frac{6+4}{3}=b \\ \\ \frac{10}{3}=b \\ \\ b=\frac{10}{3} \end{gathered}$

Therefore, the equation of the parallel line in slope-intercept form is:

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

ANSWER:

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