Question

write an equation in slope intercept form of the line that passes through the given point and is parallel to the graph of the equation(-3, -5); y = -5x+2

Answer 1

The equation is y = -5x-20.

GIven:

The equation is, y = -5x + 2.

A point on the line is (-3, 5).

The objective is to write an equation that passes throught the point and parallel to the given equation.

For parallel lines the product of slope values will be equal.

From the given equation, consider the slope of the equation as, m1 = -5.

Then, the slope of the parallel line will also be, m2 = -5.

Then, the equation of parallel line can be written as,

`\begin{gathered} y=m_2x+b \\ y=-5x+b \end{gathered}`

Here b represents the y intercept of the parellel line.

To find the value of b, substitute the given points in the above equation.

`\begin{gathered} -5=-5(-3)+b \\ -5=15+b \\ b=-5-15 \\ b=-20 \end{gathered}`

Now, substitute the value of b in the equation of parellel line.

`y=-5x-20`

Hence, the equation of parellel line is y = -5x-20.