Audrey is trying to find the equation of a line parallel to y = 2 over 3x _5 in slope-intercept form that passes through the point (_6, _1). Which of the following equations will she use?

y − (−6) = 2 over 3(x − (−1))

y − (−1) = 2 over 3(x − (−6))

y − (−6) = 3 over 2(x − (−1))

y − (−1) = 3 over 2(x − (−6))

A line parallel to y = 2/3 x - 5 will have a slope of 2/3.
The equation of a line passing through (-6, -1) with a slope of 2/3 is
y - (-1) = 2/3 (x - (-6))

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ColinJacobus ColinJacobus · Answer 2 · 2019-04-17T10:42:25-04:00

Answer: The correct option is

(B) \(y-(-1)=\dfrac{2}{3}(x-(-6)).\)

Step-by-step explanation: Given that Audrey is trying to find the equation of a line parallel to \(y=\dfrac{2}{3}x-5\) in slope-intercept form that passes through the point (-6, -1).

We are to find the equation of the line that she use.

The given line is

\(y=\dfrac{2}{3}x-5~~~~~~~~~~~~~~~~~~~~~~~(i)\)

Comparing the above equation with the slope-intercept form \(y=mx+c,\), we have

\(\textup{slope, m}=\dfrac{2}{3}.\)

We know that the slopes of two parallel lines are equal.

So, the slope of the new line will also be

\(m=\dfrac{2}{3}.\)

Since the line passes through the point (-6, -1), so its equation will be

\(y-(-1)=m(x-(-6))\\\\\\\Rightarrow y-(-1)=\dfrac{2}{3}(x-(-6)).\)

Thus, the required equation of the line is

\(y-(-1)=\dfrac{2}{3}(x-(-6)).\)

Option (B) is CORRECT.