Questions: Find an equation for the line below.

Transcript text: Find an equation for the line below.

Solution

Step 1: Identify Two Points on the Line

From the graph, identify two points that the line passes through. Let's choose the points (-4, -2) and (2, 4).

Step 2: Calculate the Slope (m)

Use the slope formula \( m = \frac{y_2 - y_1}{x_2 - x_1} \): \[ m = \frac{4 - (-2)}{2 - (-4)} = \frac{4 + 2}{2 + 4} = \frac{6}{6} = 1 \]

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

Use the point-slope form \( y - y_1 = m(x - x_1) \) with one of the points, say (2, 4): \[ y - 4 = 1(x - 2) \]

Step 4: Simplify to Slope-Intercept Form

Simplify the equation to the slope-intercept form \( y = mx + b \): \[ y - 4 = x - 2 \] \[ y = x + 2 \]

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

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