Questions: of the line shown on the graph in slope 5.

of the line shown on the graph in slope 5.
Transcript text: of the line shown on the graph in slope 5.
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Solution

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Solution Steps

Step 1: Identify two points on the line

From the graph, we can identify two points on the line. Let's choose the points (0, -2) and (2, 2).

Step 2: Calculate the slope

The slope \( m \) of a line passing through two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \]

Substituting the points (0, -2) and (2, 2): \[ m = \frac{2 - (-2)}{2 - 0} = \frac{2 + 2}{2} = \frac{4}{2} = 2 \]

Step 3: Write the equation in slope-intercept form

The slope-intercept form of a line is given by: \[ y = mx + b \]

We already have the slope \( m = 2 \). To find the y-intercept \( b \), we use one of the points, say (0, -2): \[ y = 2x + b \] \[ -2 = 2(0) + b \] \[ b = -2 \]

Final Answer

The equation of the line in slope-intercept form is: \[ y = 2x - 2 \]

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