Question: Use the slope and y-intercept to form the graph. \[ y = 2 - 7x \]

Use the slope and y-intercept to form the graph.

\[ y = 2 - 7x \]

Solution

To find the slope and y-intercept from the equation and form the graph, we start by comparing the given equation with the slope-intercept form of a line: The equation is: \[ y = 2 - 7x \] Reorder the equation to match the slope-intercept form \(y = mx + b\): \[ y = -7x + 2 \] Here, the slope \(m = -7\) and the y-intercept \(b = 2\). This means the line crosses the y-axis at 2 and has a slope of -7, indicating that for every unit increase in \(x\), \(y\) decreases by 7 units. You can use this information to graph the line. Start at the y-intercept (0, 2) and use the slope to find another point by going down 7 units and 1 unit to the right, marking this new point, and drawing the line through these points.