Question

1.) observe the given graph and check the statements that are true. (click all the apply)
the slope is negative
$m=\frac{1}{-2}$
the y-intercept is (0,0)
the slope is 2
the equation of the line is $y = -2x - \frac{1}{2}$
the line contains the point (-3, 5)
intercepts the x-axis at -0.5

2.) write the equation of the line in slope-intercept form.

3.) determining if lines are parallel or perpendicular.
slope
line a
line b
line c

Explanation:

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1.1 True Statements Check

Step1: Calculate slope

Pick two points: $(-3,5)$ and $(0,-1)$. Slope formula: $m=\frac{y_2-y_1}{x_2-x_1}$
$m=\frac{-1-5}{0-(-3)}=\frac{-6}{3}=-2$

Step2: Identify y-intercept

The line crosses y-axis at $(0,-1)$, so $b=-1$

Step3: Verify x-intercept

Set $y=0$: $0=-2x-1 \implies x=-\frac{1}{2}=-0.5$

Step4: Test point $(-3,5)$

Substitute into $y=-2x-1$: $-2(-3)-1=6-1=5$, which matches.
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2. Slope-Intercept Equation

Step1: Use slope and intercept

Slope $m=-2$, y-intercept $b=-1$. Slope-intercept form: $y=mx+b$
$y=-2x-1$
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3. Slopes of Lines a, b, c

Step1: Slope of Line a

Pick two points: rise=1, run=2. $m=\frac{1}{2}$

Step2: Slope of Line b

Pick two points: rise=3, run=1. $m=\frac{3}{1}=3$

Step3: Slope of Line c

Pick two points: rise=1, run=2. $m=\frac{1}{2}$

Answer:

1.1 True statements:

• The slope is negative
• The line contains the point (-3, 5)
• Intercepts the x-axis at -0.5

2.) $y=-2x-1$

3.)

	SLOPE
Line b	$3$
Line c	$\frac{1}{2}$