Questions: The equation of the line is:

Transcript text: The equation of the line is: $\square$

Solution

Solution Steps

Step 1: Identify Two Points on the Line

From the graph, identify two points that the line passes through. Let's choose the points (0, -5) and (5, 0).

Step 2: Calculate the Slope (m)

Use the slope formula $ m = \frac{y_2 - y_1}{x_2 - x_1} $: \[ m = \frac{0 - (-5)}{5 - 0} = \frac{5}{5} = 1 \]

Step 3: Use the Point-Slope Form to Find the Equation

Use the point-slope form of the equation of a line $ y - y_1 = m(x - x_1) $ with one of the points, say (0, -5): \[ y - (-5) = 1(x - 0) \] \[ y + 5 = x \]

Step 4: Simplify to Slope-Intercept Form

Solve for $ y $ to get the equation in slope-intercept form $ y = mx + b $: \[ y = x - 5 \]

Final Answer

The equation of the line is: \[ y = x - 5 \]

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