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Linear Equations

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Linear Equations - Forms of a Line


The graph of the line \(y=ax+b\) passes through point \((2, 90)\). If \(x\) decreases from \(3\) to \(1\), then \(y\) decreases by \(4\). What is the sum of the \(x\)-intercept and the \(y\)-intercept?

What is the equation of a line that passes through two points \((-2,-2)\) and \((4, 1)\)?

Let \(ax-y-b=0\) be the equation of the line passing through the midpoint of the line segment connecting two points \(P=(4,9)\) and \(Q=(5,1)\). If the line has slope \(6\), what is the value of \(a+b\)?

Suppose \(A\) and \(B\) are points in the first quadrant such that the slopes of the line segments \(\overline{OA}\) and \(\overline{OB}\) are \(3\) and \(\displaystyle \frac{1}{3}\), respectively, where \(O\) is the origin. If \(\lvert \overline{OA} \rvert= \lvert \overline{OB} \rvert,\) then what is the equation of line which is parallel to the line segment \(AB\) and passes through the point \(P=(-3,7)?\)

What is the equation of a line with slope \(4\) and \(y\)-intercept \(6?\)


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