Question

1. use the equation y = -3x to complete the table of values. plot the points and use them to sketch a right triangle.

how does the picture on the graph prove that the slope is -3?
the picture proves the slope is -3 because...

1. find the slope of the graph.

process:

• pick 2 points.
• one point is already chosen for you. what is it called?
• draw a triangle, create a table, or use the slope formula to find the slope.

m = __________

Explanation:

Step1: Complete the table for \(y = - 3x\)

When \(x=-2\), \(y=-3\times(-2) = 6\); when \(x = - 1\), \(y=-3\times(-1)=3\); when \(x = 0\), \(y=-3\times0 = 0\); when \(x = 1\), \(y=-3\times1=-3\); when \(x = 2\), \(y=-3\times2=-6\).

Step2: Explain slope - 3 from the graph

For a line \(y = mx + b\) (here \(b = 0\) and \(m=-3\)), the slope \(m=\frac{\Delta y}{\Delta x}\). On the graph, for every 1 - unit increase in \(x\) (right - ward movement), \(y\) decreases by 3 units (down - ward movement). So the ratio of the vertical change (\(\Delta y\)) to the horizontal change (\(\Delta x\)) is \(\frac{-3}{1}=-3\).

Step3: Find slope of the second graph

Let's pick two points. Suppose one point is \((0,2)\) (the y - intercept). Let's pick another point, say \((2,4)\). Using the slope formula \(m=\frac{y_2 - y_1}{x_2 - x_1}\), where \((x_1,y_1)=(0,2)\) and \((x_2,y_2)=(2,4)\). Then \(m=\frac{4 - 2}{2-0}=\frac{2}{2}=1\).

Answer:

\(x\)	\(y\)
- 1	3
0	0
1	- 3
2	- 6

The picture proves the slope is - 3 because for every 1 unit increase in \(x\), \(y\) decreases by 3 units.

The slope of the second graph \(m = 1\)