Slope and Graphing Linear Functions: math test solutions, Grade 9 – download the PDF

1 Slopes of lines / 4 pts

1. \(m=\dfrac{10-2}{1-(-3)}=\dfrac84=2\) (1 pt)
2. \(m=\dfrac{7-(-5)}{-2-4}=\dfrac{12}{-6}=-2\) (1 pt)
3. The \(x\)-values are equal: the slope is undefined (1 pt)
4. \(m=\dfrac{3-3}{2-(-7)}=0\) (1 pt)

2 Slope-intercept form / 3 pts

1. \(m=\dfrac{2-(-4)}{3-0}=2\) (1 pt); the \(y\)-intercept is \(-4\), so \(y=2x-4\) (1 pt).
2. \(y=2\times 10-4=16\) (1 pt).

3 Standard form and intercepts / 4 pts

1. If \(y=0\): \(3x=24\), \(x=8\), giving \((8,\,0)\) (1 pt). If \(x=0\): \(-4y=24\), \(y=-6\), giving \((0,\,-6)\) (1 pt).
2. Plot \((8,\,0)\) and \((0,\,-6)\) and draw the line through them (1 pt).
3. \(-4y=-3x+24\), so \(y=\dfrac34x-6\) and the slope is \(\dfrac34\) (1 pt).

4 Point-slope form / 3 pts

Point-slope form: \(y-1=-\dfrac32(x-4)\) (2 pts).

Expanding: \(y=-\dfrac32x+6+1=-\dfrac32x+7\) (1 pt). Check: \(-6+7=1\).

5 Parallel and perpendicular / 3 pts

1. Same slope \(-2\): \(y-4=-2(x-1)\), so \(y=-2x+6\) (1 pt).
2. The perpendicular slope is \(\dfrac12\) (1 pt): \(y-3=\dfrac12(x-4)\), so \(y=\dfrac12x+1\) (1 pt).

6 Printing pages / 3 pts

1. \(k=\dfrac{45}{3}=15\) pages per minute (1 pt).
2. \(p=15t\); for \(t=8\): \(p=120\) pages (1 pt).
3. \(15t=90\), so \(t=6\) minutes (1 pt).