Question

Line c has an equation of y = 4x + 9. Line dis parallel to line c and passes through (-4,-4).

What is the equation of line d?
Write the equation in slope-intercept form. Write the numbers in the equation as simplified
proper fractions, improper fractions, or integers.

Answer 1

`\large\boxed{\sf y = 5x +16}`

Explanation:

Here it is given that a line c has a equation of ,

`\sf\qquad\longrightarrow y = 4x + 9`

And there is another line d which is parallel to line c and passes through the point (-4,-4) . And we need to find out the equation of the line .

Firstly we know that the slope of two parallel lines is same . So on comparing the given line to the slope intercept form of the line which is y = mx + c , we have ;

`\sf\qquad\longrightarrow m = 4`

Therefore the slope of the parallel line will be ,

`\sf\qquad\longrightarrow m_(||)= 4`

On using the point slope form of the line , we have ;

`\sf\qquad\longrightarrow y - y_1 = m(x-x_1)\\`

Substitute the values ,

`\sf\qquad\longrightarrow y - (-4) = 5\{ x -(-4)\}`

Simplify ,

`\sf\qquad\longrightarrow y +4 = 5(x +4)`

Open the brackets ,

`\sf\qquad\longrightarrow y + 4 = 5x + 20`

Subtract 4/on both sides ,

`\sf\qquad\longrightarrow y = 5x +20-4`

Simplify ,

`\sf\qquad\longrightarrow \pink{ y = 5x + 16}`

Hence the equation of the line is y = 5x + 16