Question

unit 4 study guide
functions
write the equation of the line based on the graphs below. show work for the slope and y - intercept.
26.
graph of a line on a coordinate grid
28.
graph of another line on a coordinate grid

Explanation:

Problem 26:

Step1: Identify y-intercept

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

Step2: Calculate slope

Pick two points: $(-4, 1)$ and $(0, -1)$.
Slope formula: $m = \frac{y_2 - y_1}{x_2 - x_1}$
$m = \frac{-1 - 1}{0 - (-4)} = \frac{-2}{4} = -\frac{1}{2}$

Step3: Write line equation

Use slope-intercept form $y = mx + b$
$y = -\frac{1}{2}x - 1$

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Problem 28:

Step1: Identify y-intercept

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

Step2: Calculate slope

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

Step3: Write line equation

Use slope-intercept form $y = mx + b$
$y = \frac{1}{3}x + 1$

Answer:

1. $y = -\frac{1}{2}x - 1$
2. $y = \frac{1}{3}x + 1$