Slope: \(m = \frac{0 - 2}{3 - 0} = -\frac{2}{3}\)
y-intercept: \(b = 2 \implies y = -\frac{2}{3}x + 2\)
CARD 03: Answer D y = x - 4
Plotted Points: \((0, -4)\) and \((4, 0)\)
Slope: \(m = \frac{0 - (-4)}{4 - 0} = \frac{4}{4} = 1\)
y-intercept: \(b = -4 \implies y = x - 4\)
CARD 04: Answer H y = (3/4)x
Plotted Points: \((0, 0)\) and \((4, 3)\)
Slope: \(m = \frac{3 - 0}{4 - 0} = \frac{3}{4}\)
Direct variation: \(b = 0 \implies y = \frac{3}{4}x\)
CARD 05: Answer A f(x) = -2x + 1
Plotted Points: \((0, 1)\) and \((2, -3)\)
Slope: \(m = \frac{-3 - 1}{2 - 0} = \frac{-4}{2} = -2\)
Function Form: \(b = 1 \implies f(x) = -2x + 1\)
CARD 06: Answer J 2x + 3y = 6
Intercepts: \((0, 2)\) and \((3, 0)\)
Slope-Intercept: \(y = -\frac{2}{3}x + 2\)
Standard Form: Multiply by 3 \(\implies 2x + 3y = 6\)
CARD 07: Answer B y = (1/3)x + 1
Plotted Points: \((0, 1)\) and \((3, 2)\)
Slope: \(m = \frac{2 - 1}{3 - 0} = \frac{1}{3}\)
y-intercept: \(b = 1 \implies y = \frac{1}{3}x + 1\)
CARD 08: Answer F y = -3x + 2
Plotted Points: \((0, 2)\) and \((1, -1)\)
Slope: \(m = \frac{-1 - 2}{1 - 0} = \frac{-3}{1} = -3\)
y-intercept: \(b = 2 \implies y = -3x + 2\)
TEKS A.2(C) Master Key
Algebra 1 Resource
Instructional Support Guide
CARD 09: Answer C y = (3/4)x - 2
Plotted Points: \((0, -2)\) and \((4, 1)\)
Slope: \(m = \frac{1 - (-2)}{4 - 0} = \frac{3}{4}\)
y-intercept: \(b = -2 \implies y = \frac{3}{4}x - 2\)
CARD 10: Answer H y = (1/2)x - 3
Plotted Points: \((0, -3)\) and \((4, -1)\)
Slope: \(m = \frac{-1 - (-3)}{4 - 0} = \frac{2}{4} = \frac{1}{2}\)
y-intercept: \(b = -3 \implies y = \frac{1}{2}x - 3\)
CARD 11: Answer A 3x - 2y = 6
Intercepts: \((0, -3)\) and \((2, 0)\)
Slope: \(m = \frac{0 - (-3)}{2 - 0} = \frac{3}{2}\)
Standard Form: \(y = \frac{3}{2}x - 3 \implies 3x - 2y = 6\)
CARD 12: Answer G y = -(2/3)x
Plotted Points: \((0, 0)\) and \((3, -2)\)
Slope: \(m = \frac{-2 - 0}{3 - 0} = -\frac{2}{3}\)
Direct variation: \(b = 0 \implies y = -\frac{2}{3}x\)
CARD 13: Answer D y = -(3/4)x + 3
Plotted Points: \((0, 3)\) and \((4, 0)\)
Slope: \(m = \frac{0 - 3}{4 - 0} = -\frac{3}{4}\)
y-intercept: \(b = 3 \implies y = -\frac{3}{4}x + 3\)
CARD 14: Answer F y - 1 = (3/2)(x - 2)
Points: \((2, 1)\) and \((0, -2)\)
Slope: \(m = \frac{1 - (-2)}{2 - 0} = \frac{3}{2}\)
Point-Slope Form: \(y - y_1 = m(x - x_1)\) at \((2, 1)\)
CARD 15: Answer B x + y = 4
Intercepts: \((0, 4)\) and \((4, 0)\)
Slope: \(m = \frac{0 - 4}{4 - 0} = -1\)
Standard Form: \(y = -x + 4 \implies x + y = 4\)
CARD 16: Answer J f(x) = -(3/2)x + 1
Plotted Points: \((0, 1)\) and \((2, -2)\)
Slope: \(m = \frac{-2 - 1}{2 - 0} = -\frac{3}{2}\)
Function Form: \(b = 1 \implies f(x) = -\frac{3}{2}x + 1\)
1. Run over Rise Trap (Inverted Slope): Students calculate \(\frac{\Delta x}{\Delta y}\) instead of \(\frac{\Delta y}{\Delta x}\). Highlighted in Cards 02 (G vs F), 04 (F vs H), 07 (A vs B), and 09 (B vs C).
2. Sign Inversion on Negative Lines: Failing to note downward slope from left to right. Seen in Cards 01 (A vs C), 05 (B vs A), 08 (G vs F), and 13 (A vs D).
3. Standard Form Sign Traps (\(Ax \pm By = C\)): Converting \(y = mx + b\) to \(Ax + By = C\). Test by substituting both intercepts \((0, b)\) and \((a, 0)\) into each equation option (Cards 06, 11, 15).
4. Point-Slope Signs (\(y - y_1 = m(x - x_1)\)): Confusing subtraction with addition when plugging in positive coordinate values (Card 14 choice G vs F).
