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Sagot :
Answer:
The equation of the line that is parallel to
[tex]y=4x+2[/tex]and passes through (5,-
Explanation:
We want to find the standard form equation of the line that is parallel to
[tex]y=4x+2\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots.(1)[/tex]and passes through the points (5, -5)
The equation of the line given above has slope of 4 units, and y-intercept of 2.
Any equation with the slope 4 units and a different y-intercept from 2 - is a parallel line with the line in equation (1).
Let this parallel line be:
[tex]y=4x+b\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots.(2)[/tex]Since this line passes through (5, -5), we have x = 5, and y = -5. Substituting these valeus of x and y in equation (2), we can easily find the value of the y-intercept b
[tex]\begin{gathered} -5=4(5)+b \\ \\ -5=20+b \\ \\ \text{Subtract 20 from both sides} \\ -5-20=b \\ b=-25 \end{gathered}[/tex]Therefore, the equation of the line is:
[tex]y=4x-25[/tex]
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