Question

Option 4: y= 3/5x - 42/5

Thank you

Answer 1

Explanation:

The equation of line B will be
`y=(3)/(4)x-9`

The line A passes through
`(-7,-8)(1,-2)`

Let,

`x_1=-7\\y_1=-8\\x_2=1\\y_2=-2`

As the line B is parallel to line A, the slope will be same for both the lines.

Slope of line A = slope of line B =
`m = (y_2 - y_1)/(x_2 - x_1) = (-2-(-8))/(1-(-7)) = (6)/(8)=(3)/(4)`

Since line B passes through
`(4,-6)`;

∴
`x=4 , y=-6`

`y=mx+c\\-6=(3)/(4) (4) + c\\-6=3+c\\c=-6-3\\c=-9`

Substituting above values in
`y=mx+c`

Thus, the equation of line B is
`y=(3)/(4)x-9`