1.
Which of the following best describes the lines \(\frac{1}{3}x-y=2\) and \(y+4=\frac{1}{3}x\)?
Convert both equations to slope-intercept form: \(y=\frac{1}{3}x-2\) and \(y=\frac{1}{3}x-4\). They have the same slope but different y-intercepts, so they are parallel.
2.
Two life insurance companies determine their premiums using different formulas: Company A: \(p=2a+24\); Company B: \(p=2.25a+13\). Use the graph to determine the age at which both companies charge the same premium.
The graph shows the two lines intersect at about 45 years old. Among the options, 44 years is the closest/best answer.
3.
Determine the solution of the linear system represented by the graph.
From the graph, the lines intersect at approximately \((-2,3.8)\).
4.
Which linear system is represented by this graph?
For \(x-y=3\), slope-intercept form is \(y=x-3\), so the slope is \(1\) and the y-intercept is \(-3\). For \(6x+5y=14\), slope-intercept form is \(y=-\frac{6}{5}x+\frac{14}{5}\), so the slope is \(-\frac{6}{5}\) and the y-intercept is \(2.8\). These match the graph.
5.
Choose the graph which illustrates the following system: \(x-y=0\) and \(x+2=0\).
\(x-y=0\) gives \(y=x\), a line with slope \(+1\). \(x+2=0\) gives \(x=-2\), a vertical line through \(-2\). Graph B matches these two lines.
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