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: Recall the slope-intercept form of a line: \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept. We will use the point-slope form first to find the equation of the line.
3. Step 3: Use the point-slope form formula: \(y - y_1 = m(x - x_1)\), where \((x_1, y_1)\) is the point \((-1, 5)\) and \(m = -4\). Substitute these values to get \(y - 5 = -4(x + 1)\).
4. Step 4: Simplify the equation to slope-intercept form by distributing and solving for \(y\): \(y - 5 = -4x - 4\), then \(y = -4x + 1\).
5. Step 5: To graph the line, start at the point \((-1, 5)\) on the coordinate plane. From this point, use the slope \(-4\) which means going down 4 units and right 1 unit to find another point. Draw a straight line through these points.