Question: Graph the linear equation. \[ y = 8x + 2 \]

Solution

The problem asks to graph the linear equation: \[ y = 8x + 2 \] To graph this equation, follow these steps: Find the y-intercept. The equation is in the slope-intercept form \( y = mx + b \), where \( b \) is the y-intercept. Here, \( b = 2 \). So, the y-intercept is at the point \( (0, 2) \). Determine the slope. The slope \( m \) is 8, which means for every increase of 1 in \( x \), \( y \) increases by 8. Plot the y-intercept on the graph at \( (0, 2) \). From the y-intercept, use the slope to find another point. Starting at \( (0, 2) \), move 1 unit to the right (increase in \( x \)) and 8 units up (increase in \( y \)) to get to the point \( (1, 10) \). Plot the second point at \( (1, 10) \). Draw a straight line through the two points to extend the line in both directions. This line represents the graph of the equation \( y = 8x + 2 \).