Question

1. line a has the slope $m = -\frac{d}{r}$.what is the slope of a line perpendicular to line a and why?a. $\frac{r}{d}$ because the slopes of perpendicular lines are opposite reciprocalsb. $-\frac{d}{r}$ because the slopes of perpendicular lines are the samec. $\frac{d}{r}$ because the slopes of perpendicular lines are opposited. $-\frac{r}{d}$ because the slopes of perpendicular lines are reciprocalstell whether the lines for each pair of equations are parallel, perpendicular, or neither.6. $y = -\frac{1}{4}x + 10$$-2x + 8y = 6$a. parallelb. perpendicularc. neither7. the table shows the height of an elevator above ground level after a certain amount of time. model the data with an equation. let $y$ stand for the height of the elevator in feet and let $x$ stand for the time in seconds.| time (s) | height (ft) || ---- | ---- || 10 | 156 || 20 | 142 || 40 | 114 || 60 | 86 |a. $y = -1.4x + 170$b. $y = 170x - 1.4$c. $y = -1.4 + 156$d. $y = 10x + 156$8. is the line through points $p(8, 3)$ and $q(4, 2)$ parallel to the line through points $r(-5, -5)$ and $s(-1, -2)$? explain.a. yes; the lines have equal slopes.b. yes; the lines are both vertical.c. no; the lines have unequal slopes.d. no; one line has zero slope, the other has no slope.in the following situations, is there likely to be a correlation? if so does the correlation reflect a causal relationship? explain.9. the number of hours spent studying for a test and your test marka. there is a positive correlation and also a causal relationship. the more you study for a test the better your mark is likely to be.b. there is a negative correlation. the more you study for a test, the worse your mark is likely to be.c. there is no correlation.what type of relationship does the scatter plot show?

Explanation:

Step1: Find perpendicular slope rule

Perpendicular slopes are opposite reciprocals: if slope is $m$, perpendicular slope is $-\frac{1}{m}$.

Step2: Calculate perpendicular slope

Given $m=-\frac{d}{r}$, its reciprocal is $-\frac{r}{d}$, opposite gives $\frac{r}{d}$.

Step1: Rewrite second line to slope-intercept

Rearrange $-2x+8y=6$: $8y=2x+6 \implies y=\frac{2}{8}x+\frac{6}{8} \implies y=\frac{1}{4}x+\frac{3}{4}$

Step2: Compare slopes

First line slope: $-\frac{1}{4}$, second line slope: $\frac{1}{4}$. Slopes are not equal, and product is $-\frac{1}{4} \times \frac{1}{4}=-\frac{1}{16}
eq -1$.

Step1: Calculate slope from table

Use points $(10,156)$ and $(20,142)$: $m=\frac{142-156}{20-10}=\frac{-14}{10}=-1.4$

Step2: Find y-intercept

Use $y=mx+b$, substitute $x=10,y=156,m=-1.4$: $156=-1.4(10)+b \implies 156=-14+b \implies b=170$

Step1: Calculate slope of PQ

Slope formula: $m=\frac{y_2-y_1}{x_2-x_1}$. For $P(8,3),Q(4,2)$: $m_{PQ}=\frac{2-3}{4-8}=\frac{-1}{-4}=\frac{1}{4}$

Step2: Calculate slope of RS

For $R(-5,-5),S(-1,-2)$: $m_{RS}=\frac{-2-(-5)}{-1-(-5)}=\frac{3}{4}$

Step3: Compare slopes

$\frac{1}{4}
eq \frac{3}{4}$, so lines are not parallel.

Answer:

a. r/d because the slopes of perpendicular lines are opposite reciprocals

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