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Equation of a Line

Explore how simple equations have graphical implications starting with the equation of a line.

Level 1

         

Consider the line given by the equation\[y=\frac{5}{2}x+30.\] Let \(a\) and \(b\) be the \(x\)-intercept and \(y\)-intercept of this line. What is the value of \(a+b\)?

Two lines \(y-ax=2\) and \(x+23y=138\) are perpendicular to each other. What is the value of \(a\)?

Find the equation of the line which has a slope of \(-\frac{3}{4}\) and forms a triangle with the positive coordinate axes such that the triangle has an area of 24 square units.

If three points \(A=(k,k+2),\) \(B=(0,k-6)\) and \(C=(k-4,k)\) all lie on the same line, what is the value of \(k?\)

The graph of the line \(y=ax+b\) passes through the point \((2, 90)\). Additionally, traveling along the line, if \(x\) decreases by \(2\), then \(y\) decreases by \(4\). What is the sum of the \(x\)-intercept and the \(y\)-intercept?

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