Question

Write the equation of the line passing through the given point that is parallel to the given line

1. y=2/3x - 2, (-3,4)
2.y=-2x +7y =14 (-7,-3)

Answer 1

Answer for question #1: y=
`(2x)/(3)`+ 6

Explanation:

1. Find the equation of the line parallel to the line y=2x/3−2 passing through the point (−3,4).

The equation of the line in the slope-intercept form is y=2x/3−2.

The slope of the parallel line is the same: m=23.

So, the equation of the parallel line is y=2x/3+a.

To find a, we use the fact that the line should pass through the given point: 4=(23)⋅(−3)+a.

Thus, a=6.

Therefore, the equation of the line is y=2x/3+6.

Answer: y=2x/3+6.