Question

graph the line with the equation $y = -\frac{3}{4}x - 4$.

Explanation:

Step1: Identify Slope and Intercept

The equation \( y = -\frac{3}{4}x - 4 \) is in slope - intercept form \( y=mx + b \), where \( m = -\frac{3}{4} \) (slope) and \( b=-4 \) (y - intercept). So, the line crosses the y - axis at \( (0,-4) \).

Step2: Plot the Y - Intercept

Locate the point \( (0,-4) \) on the coordinate plane.

Step3: Use the Slope to Find Another Point

The slope \( m = -\frac{3}{4}=\frac{\text{rise}}{\text{run}} \). From \( (0,-4) \), move down 3 units (because the rise is - 3) and then move right 4 units (because the run is 4). This gives the point \( (4,-7) \). Alternatively, we can move up 3 units and left 4 units from \( (0,-4) \) to get \( (-4,-1) \).

Step4: Draw the Line

Draw a straight line through the points \( (0,-4) \) and the other point (e.g., \( (4,-7) \) or \( (-4,-1) \)) to graph the line \( y = -\frac{3}{4}x - 4 \).

Answer:

To graph \( y = -\frac{3}{4}x - 4 \), plot \( (0,-4) \), then use slope \( -\frac{3}{4} \) to find another point (e.g., \( (4,-7) \) or \( (-4,-1) \)), and draw a line through them.