Question

graph the line with slope -3 passing through the point (-3, 2).

Explanation:

Step1: Use the point - slope form

The point - slope form of a line is \(y - y_1=m(x - x_1)\), where \(m\) is the slope and \((x_1,y_1)\) is a point on the line. Given \(m=-3\), \(x_1=-3\), and \(y_1 = 2\), we substitute these values into the formula:
\(y - 2=-3(x+3)\)

Step2: Simplify the equation

Expand the right - hand side: \(y - 2=-3x - 9\). Then add 2 to both sides to get the slope - intercept form \(y=-3x - 7\).

Step3: Find another point

We know one point \((-3,2)\). Using the slope \(m=-3=\frac{\Delta y}{\Delta x}\), if we let \(\Delta x = 1\), then \(\Delta y=-3\). So another point is \((-3 + 1,2-3)=(-2,-1)\)

Step4: Plot the points and draw the line

Plot the points \((-3,2)\) and \((-2,-1)\) on the coordinate plane. Then draw a straight line passing through these two points.

Answer:

Plot the point \((-3,2)\). Using the slope \(m = - 3\) (which means for a run of 1, the rise is - 3), find another point (e.g., \((-2,-1)\)) and draw a straight line through these points.