Questions: Write an equation for the line graphed below

Write an equation for the line graphed below
Transcript text: Write an equation for the line graphed below
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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 \((0, -3)\) and \((3, 3)\).

Step 2: Calculate the slope (m) of the line

The slope \(m\) is calculated using the formula: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] Substituting the points \((0, -3)\) and \((3, 3)\): \[ m = \frac{3 - (-3)}{3 - 0} = \frac{6}{3} = 2 \]

Step 3: Use the slope-intercept form to write the equation

The slope-intercept form of a line is: \[ y = mx + b \] We already have the slope \(m = 2\). To find the y-intercept \(b\), we use one of the points, say \((0, -3)\): \[ -3 = 2(0) + b \] \[ b = -3 \]

Final Answer

The equation of the line is: \[ y = 2x - 3 \]

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