Question

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

Explanation:

Step1: Identify the slope and y-intercept

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

Step2: Plot the y - intercept

The y - intercept is \(b = - 4\), so we plot the point \((0,-4)\) on the y - axis.

Step3: Use the slope to find another point

The slope \(m=-\frac{3}{4}=\frac{\text{rise}}{\text{run}}\). From the point \((0, - 4)\), we move down 3 units (because the rise is - 3, which means we move in the negative y - direction) and then move 4 units to the right (because the run is 4, positive x - direction). This gives us the point \((0 + 4,-4-3)=(4,-7)\). We can also move up 3 units and left 4 units from \((0,-4)\) to get the point \((0 - 4,-4 + 3)=(-4,-1)\).

Step4: Draw the line

Draw a straight line through the points we have plotted (e.g., \((0,-4)\) and \((4,-7)\) or \((0,-4)\) and \((-4,-1)\)).

Answer:

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