Slope of a line and angle between two lines

Correct answer: A. \(-\frac{3}{2}\)

Rearranging the equation gives \(2y=-3x+12\), so \(y=-\frac{3}{2}x+6\). In the slope-intercept form \(y=mx+c\), the coefficient of \(x\) is the slope; hence the slope is \(-\frac{3}{2}\). Option B has the wrong sign. Exam tip: For a line \(ax+by+c=0\), its slope is \(-\frac{a}{b}\).

Correct answer: A. \(-4\)

In the standard form \(y=mx+c\), the coefficient of \(x\), namely \(m\), is the slope. For \(y=-4x+9\), \(m=-4\), so the correct answer is \(-4\). Option \(4\) has the wrong sign, while \(9\) is the y-intercept, not the slope. Exam tip: In \(y=mx+c\), identify the coefficient of \(x\) directly.

Correct answer: A. \(\frac{4}{3}\)

Rewrite the equation in slope-intercept form: \(4x-3y=15\Rightarrow y=\frac{4}{3}x-5\). In \(y=mx+c\), the coefficient of \(x\) is the slope \(m\), so the slope is \(\frac{4}{3}\). The value \(\frac{3}{4}\) is its reciprocal, not the slope. Exam tip: first isolate \(y\) and compare the equation with \(y=mx+c\).