Proportionality>Representing Linear Non-Proportional Situations with Tables, Graphs, and Equations(TEKS.Math.8.5.B)
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Texas 8th Grade Math › Proportionality>Representing Linear Non-Proportional Situations with Tables, Graphs, and Equations(TEKS.Math.8.5.B)
A line is graphed on a coordinate plane. It crosses the y-axis at 4 and passes through the point (3, 10).
Which equation represents the graphed line?
$y = 4x + 2$
$y = 2x$
$y = 2x - 4$
$y = 2x + 4$
Explanation
The y-intercept is $b = 4$ (non-proportional since $b \ne 0$). Using the point (3, 10), the slope is $m = (10 - 4) / 3 = 2$. So the equation is $y = 2x + 4$. Options with $b = 0$ are proportional and do not match the intercept, and swapping $m$ and $b$ gives the wrong line.
Cell phone plan: There is a monthly fee of 25 dollars plus 0.10 dollars per text message. When x = 0 texts, the cost is 25 dollars. When x = 50 texts, the cost is 30 dollars.
Which equation represents the total monthly cost y (in dollars) for x text messages?
$y = 0.10x + 25$
$y = 25x + 0.10$
$y = 0.10x$
$y = 0.25x + 10$
Explanation
This is a non-proportional linear relationship with a fixed fee, so it fits $y = mx + b$ where $b \ne 0$. The rate is $m = 0.10$ dollars per text and the starting value is $b = 25$ dollars at $x = 0$, giving $y = 0.10x + 25$. The other choices either omit the fixed fee, swap $m$ and $b$, or use incorrect values.