Question

4 sketch the graph of each line: $y = -\frac{3}{2}x - 1$

Explanation:

Step1: Identify 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 \(y=-\frac{3}{2}x - 1\), the slope \(m =-\frac{3}{2}\) and the y - intercept \(b=- 1\).

Step2: Plot the y - intercept

The y - intercept is \((0,b)=(0, - 1)\). So we mark the point \((0,-1)\) on the coordinate plane.

Step3: Use the slope to find another point

The slope \(m =-\frac{3}{2}=\frac{\text{rise}}{\text{run}}\). The negative sign means we can go down 3 units (rise) and then right 2 units (run) from the point \((0,-1)\).
Starting from \((0,-1)\), going down 3 units (since rise is - 3) gives \(y=-1 - 3=-4\) and going right 2 units gives \(x = 0+2 = 2\). So the new point is \((2,-4)\). We can also go up 3 units and left 2 units (because \(\frac{3}{-2}\) is also equal to \(-\frac{3}{2}\)). Starting from \((0,-1)\), going up 3 units gives \(y=-1 + 3 = 2\) and going left 2 units gives \(x=0 - 2=-2\). So the point \((-2,2)\) is also on the line.

Step4: Draw the line

Using a straight - edge, draw a line through the points \((0,-1)\), \((2,-4)\) (or \((-2,2)\) and \((0,-1)\)) to sketch the graph of the line \(y =-\frac{3}{2}x-1\).

Answer:

The graph of the line \(y =-\frac{3}{2}x - 1\) is drawn by first plotting the y - intercept \((0,-1)\) and then using the slope \(-\frac{3}{2}\) to find additional points (such as \((2,-4)\) or \((-2,2)\)) and drawing a straight line through these points.