Graph the line having a slope of $-4$ and passes through $(-1,5)$.

• A.
• B.
• C.
• D.

Answer: (C)

Verified step by step guidance

1. Step 1: Identify the given slope and point. The slope is \(-4\) and the point the line passes through is \((-1, 5)\).
2. Step 2: Use the point-slope form of the equation of a line: \(y - y_1 = m(x - x_1)\), where \(m\) is the slope and \((x_1, y_1)\) is the given point. Substitute \(m = -4\), \(x_1 = -1\), and \(y_1 = 5\) to get \(y - 5 = -4(x + 1)\).
3. Step 3: Simplify the equation to slope-intercept form \(y = mx + b\) by distributing and isolating \(y\). This gives \(y - 5 = -4x - 4\), so \(y = -4x + 1\).
4. Step 4: Plot the point \((-1, 5)\) on the coordinate plane as the starting point.
5. Step 5: Use the slope \(-4\) to find another point. Since slope is rise over run, from \((-1, 5)\) move down 4 units and right 1 unit to plot the next point. Draw a line through these points to graph the line.