**Title: Writing Equations of Lines** **Instruction:** Write an equation for the graph below in terms of \( x \). **Graph Description:** - The graph appears to show a straight line on a coordinate plane. - The x-axis and y-axis both range from -5 to 5. - The line passes through the point at (-2, 0) and the point at (2, 4). **Line Details:** The line has a positive slope, indicating that as \( x \) increases, \( y \) also increases. **Finding the Equation:** To find the equation of the line, use the slope-intercept form: \[ y = mx + b \] Where: - \( m \) is the slope of the line. - \( b \) is the y-intercept. **Calculating the Slope (\( m \)):** The slope \( m \) is calculated as: \[ m = \frac{\Delta y}{\Delta x} = \frac{y_2 - y_1}{x_2 - x_1} \] Substituting the points (-2, 0) and (2, 4) into the formula: \[ m = \frac{4 - 0}{2 - (-2)} = \frac{4}{4} = 1 \] **Determining the Y-intercept (\( b \)):** The line intersects the y-axis at the point where \( x = 0 \). Observing the graph, this occurs at: \[ b = 2 \] **Equation of the Line:** Therefore, the equation of the line is: \[ y = x + 2 \] **Input Section:** Use the input box below to enter your equation. **Question Help:** Need assistance? [Message Instructor] **Submission:** Press the "Submit Question" button to submit your answer. **Submit Question: [Button]** --- This exercise helps students practice finding the equation of a line using given points and understanding the relationship between a graph and its algebraic representation.

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