Question

write an equation for each line in slope-intercept form.

(first graph: line on coordinate grid) equation: _______________

(second graph: line on coordinate grid) equation: _______________

(third graph: line on coordinate grid) equation: _______________

(fourth graph: line on coordinate grid) equation: _______________

Explanation:

Line 1 (Top Left)

Step1: Identify y-intercept

The line crosses the y-axis at $b=3$.

Step2: Calculate slope

Use points $(0,3)$ and $(6,1)$.
$m=\frac{1-3}{6-0}=\frac{-2}{6}=-\frac{1}{3}$

Step3: Write slope-intercept form

$y=mx+b$
$y=-\frac{1}{3}x+3$

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Line 2 (Top Right)

Step1: Identify y-intercept

The line crosses the y-axis at $b=0$.

Step2: Calculate slope

Use points $(0,0)$ and $(2,1)$.
$m=\frac{1-0}{2-0}=\frac{1}{2}$

Step3: Write slope-intercept form

$y=mx+b$
$y=\frac{1}{2}x$

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Line 3 (Bottom Left)

Step1: Identify y-intercept

The line crosses the y-axis at $b=3$.

Step2: Calculate slope

Use points $(0,3)$ and $(-3,0)$.
$m=\frac{0-3}{-3-0}=\frac{-3}{-3}=1$

Step3: Write slope-intercept form

$y=mx+b$
$y=x+3$

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Line 4 (Bottom Right)

Step1: Identify y-intercept

The line crosses the y-axis at $b=4$.

Step2: Calculate slope

Use points $(0,4)$ and $(2,0)$.
$m=\frac{0-4}{2-0}=\frac{-4}{2}=-2$

Step3: Write slope-intercept form

$y=mx+b$
$y=-2x+4$

Answer:

Top Left: $y=-\frac{1}{3}x+3$
Top Right: $y=\frac{1}{2}x$
Bottom Left: $y=x+3$
Bottom Right: $y=-2x+4$