Question

name ______ date ____ block ______
math 1b hw: graphing lines using slope / slope-int. form
count the slope for each section of the roller coaster.

1. which section is the steepest, section 4, 5, or 6? explain / verify your answer using the slope.

error analysis: find and explain the error in the slope formula below.

1. $(20,6),(-2,6)$

$m=\frac{6-6}{-2-20}$
$=\frac{0}{-22}=undefined$

1. graph the line thru $(-4,-2)$, with a slope of $\frac{4}{7}$.

Explanation:

Step1: Compare absolute slopes

Section 4: $|\frac{6}{12}|=0.5$; Section 5: $|\frac{6}{3}|=2$; Section 6: $|\frac{4}{6}|\approx0.67$

Step2: Identify steepest section

2 is the largest absolute slope.

Step1: Check slope formula setup

Slope formula is $m=\frac{y_2-y_1}{x_2-x_1}$.

Step2: Locate sign error

For points $(20,6)$ and $(-2,6)$, $x_2-x_1=-2-20=-22$, but $y_2-y_1=6-6=0$. The error is mislabeling the $x$-values in the denominator (swapped signs incorrectly) and misstating the final result: $\frac{0}{-22}=0$, not undefined. Undefined slope is for vertical lines, but this is a horizontal line.

Step1: Plot the starting point

Mark the point $(-4,-2)$ on the coordinate grid.

Step2: Use slope to find next point

Slope $\frac{4}{7}$ means rise 4, run 7. From $(-4,-2)$, move up 4 units to $y=-2+4=2$, right 7 units to $x=-4+7=3$, so the new point is $(3,2)$.

Step3: Draw the line

Connect $(-4,-2)$ and $(3,2)$ with a straight line, extending it in both directions.

Answer:

Section 5 is the steepest. Its absolute slope is 2, which is greater than the absolute slopes of section 4 (0.5) and section 6 (≈0.67). A larger absolute slope means a steeper line.

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