Graph the line represented by the equation $y=-\frac{4}{5}x+2$

• A.
• B.
• C.
• D.

Answer: (C)

Verified step by step guidance

1. Identify the equation of the line given: \(y = -\frac{4}{5}x + 2\). This is in slope-intercept form \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept.
2. Locate the y-intercept \(b = 2\) on the graph. This is the point where the line crosses the y-axis, so plot the point \((0, 2)\).
3. Use the slope \(m = -\frac{4}{5}\) to find another point. The slope means that for every 5 units you move to the right (positive direction on the x-axis), you move 4 units down (negative direction on the y-axis). Starting from \((0, 2)\), move right 5 units to \(x=5\) and down 4 units to find the point \((5, -2)\).
4. Plot the second point \((5, -2)\) on the graph. This confirms the direction and steepness of the line.
5. Draw a straight line through the points \((0, 2)\) and \((5, -2)\) extending across the graph. This line represents the equation \(y = -\frac{4}{5}x + 2\).