Question

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))

Answer 1

Answer: The correct option is

(B)
`y-(-1)=(2)/(3)(x-(-6)).`

Step-by-step explanation: Given that Audrey is trying to find the equation of a line parallel to
`y=(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=(2)/(3)x-5~~~~~~~~~~~~~~~~~~~~~~~(i)`

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

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

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

So, the slope of the new line will also be

`m=(2)/(3).`

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

`y-(-1)=m(x-(-6))\\\\\\\Rightarrow y-(-1)=(2)/(3)(x-(-6)).`

Thus, the required equation of the line is

`y-(-1)=(2)/(3)(x-(-6)).`

Option (B) is CORRECT.

Answer 2

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))