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} (-3y)/(-3)=(-2x)/(-3)+(7)/(-3) \\ \\ y=(2)/(3)x-(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=(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=(2)/(3)(-2)+b \\ \\ 2=(2*(-2))/(3)+b \\ \\ 2=-(4)/(3)+b \end{gathered}`

Add 4/3 to both sides:

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

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

`y=(2)/(3)x+(10)/(3)`

ANSWER:

`y=(2)/(3)x+(10)/(3)`