Question

graph the line passing through the given point and having the indicated slope. through (-1,0) with slope -2/3 use the graphing tool on the right to graph the line. click to enlarge graph

Explanation:

Step1: Recall the slope formula

The slope \(m =-\frac{2}{3}\) can be written as \(m=\frac{\Delta y}{\Delta x}\), where \(\Delta y=- 2\) and \(\Delta x = 3\) (or \(\Delta y = 2\) and \(\Delta x=-3\)).

Step2: Find another point

Starting from the point \((-1,0)\). If we use \(\Delta x = 3\) and \(\Delta y=-2\), then the new \(x\) - coordinate is \(x=-1 + 3=2\) and the new \(y\) - coordinate is \(y=0-2=-2\), so we get the point \((2,-2)\). If we use \(\Delta x=-3\) and \(\Delta y = 2\), then the new \(x\) - coordinate is \(x=-1-3=-4\) and the new \(y\) - coordinate is \(y=0 + 2=2\), so we get the point \((-4,2)\).

Step3: Plot the points and draw the line

Plot the point \((-1,0)\), \((2,-2)\) (or \((-4,2)\)). Then use a straight - edge to draw a line passing through these points.

Answer:

Plot the point \((-1,0)\). From \((-1,0)\), move 3 units to the right and 2 units down to get \((2,-2)\) (or 3 units to the left and 2 units up to get \((-4,2)\)), then draw a line through the points.