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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))

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nobillionaireNobley
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))

Answer:  The correct option is

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

Step-by-step explanation:  Given that Audrey is trying to find the equation of a line parallel to [tex]y=\dfrac{2}{3}x-5[/tex] 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

[tex]y=\dfrac{2}{3}x-5~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]

Comparing the above equation with the slope-intercept form [tex]y=mx+c,[/tex], we have

[tex]\textup{slope, m}=\dfrac{2}{3}.[/tex]

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

So, the slope of the new line will also be

[tex]m=\dfrac{2}{3}.[/tex]

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

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

Thus, the required equation of the line is

[tex]y-(-1)=\dfrac{2}{3}(x-(-6)).[/tex]

Option (B) is CORRECT.

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