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valkas [14]
3 years ago
15

PLEASE ANSWER THIS ASAP

Mathematics
1 answer:
Arisa [49]3 years ago
3 0

Answer:

The equation of line passes through (4,-1) and perpendicular to the graph y=\frac{7}{2}x-\frac{3}{2} is y=\frac{-2x}{7}+\frac{1}{7}

Step-by-step explanation:

Given point is (4,-1) and equation of line is y=\frac{7}{2}x-\frac{3}{2}

Let the slope of line that passes through point (4,-1) is m_1

And slope of line y=\frac{7}{2}x-\frac{3}{2} is m_2=\frac{7}{2} . As it is in the form of y=mx+c

We know the relation between slope of perpendicular line are given by

m_1\times m_2=-1\\And\ m_1=\frac{-1}{m_2}

So, the slope m_1=\frac{-1}{\frac{7}{2}}=\frac{-2}{7}

Now, we can write the equation of line having point  (4,-1) and slope \frac{-2}{7}

(y-y_1)=m(x-x_1)\\\\(y-(-1))=\frac{-2}{7}(x-4)\\\\y+1=\frac{-2x}{7}-(\frac{2\times -4}{7})\\ \\y+1=\frac{-2x}{7}+\frac{8}{7}\\\\y=\frac{-2x}{7}+\frac{8}{7}-1\\\\y=\frac{-2x}{7}+\frac{8-7}{7}\\\\y=\frac{-2x}{7}+\frac{1}{7}

So, the equation of line passes through (4,-1) and perpendicular to the graph y=\frac{7}{2}x-\frac{3}{2} is y=\frac{-2x}{7}+\frac{1}{7}

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