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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.

Sagot :

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Answer:

[tex]\large\boxed{\sf y = 5x +16}[/tex]

Step-by-step explanation:

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

[tex]\sf\qquad\longrightarrow y = 4x + 9[/tex]

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 ;

[tex]\sf\qquad\longrightarrow m = 4 [/tex]

Therefore the slope of the parallel line will be ,

[tex]\sf\qquad\longrightarrow m_{||}= 4 [/tex]

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

[tex]\sf\qquad\longrightarrow y - y_1 = m(x-x_1)\\ [/tex]

Substitute the values ,

[tex]\sf\qquad\longrightarrow y - (-4) = 5\{ x -(-4)\} [/tex]

Simplify ,

[tex]\sf\qquad\longrightarrow y +4 = 5(x +4)[/tex]

Open the brackets ,

[tex]\sf\qquad\longrightarrow y + 4 = 5x + 20 [/tex]

Subtract 4/on both sides ,

[tex]\sf\qquad\longrightarrow y = 5x +20-4 [/tex]

Simplify ,

[tex]\sf\qquad\longrightarrow \pink{ y = 5x + 16} [/tex]

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

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