Question

Write the equation of the line that passes through (-1, 8) and is parallel to the line that passes through (5, -1) and (2, -5).

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Answer 1

`\large\boxed{y=-(3)/(4)x+(29)/(4)}`

Explanation:

`\text{Let}\\\\k:y=m_1x+b_1,\ l:y=m_2x+b_2\\\\k\ ||\ l\iff m_1=m_2\\\\k\ \perp\ l\iff m_1m_2=-1\to m_2=-(1)/(m_1)\\\\=================================`

`\text{The formula of a slope:}\\\\m=(y_2-y_1)/(x_2-x_1)`

`\text{Calculate the slops:}\\\\(5,\ -1),\ (2,\ -5)\\\\m_1=(-5-(-1))/(2-5)=(-5+1)/(-3)=(-4)/(-3)=(4)/(3)\\\\\text{Therefore}\\\\m_2=-(1)/((4)/(3))=-1\left((3)/(4)\right)=-(3)/(4)\\\\\text{Put the value of slope and coordinates of the given point (-1, 8) }\\\text{to the equation of a line:}\\\\8=-(3)/(4)(-1)+b\\\\8=(3)/(4)+b\qquad\text{subtract}\ (3)/(4)\ \text{from both sides}\\\\7(1)/(4)=b\to b=(29)/(4)\\\\\text{Finally:}\\\\y=-(3)/(4)x+(29)/(4)`