Question

find the slope of the graph and the equation. do they have the same slopes?
draw
slope of graph = 1
slope of equation = 1
yes, the slopes are the same. no, the slopes are not the same

Explanation:

Step1: Identify two points on the graph

Looking at the graph, we can pick two points, for example, \((0, -2)\) and \((2, 0)\). (We can also use other points like \((1, -1)\) and \((3, 1)\), but these two are clear from the grid.)

Step2: Calculate the slope of the graph

The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Using the points \((0, -2)\) and \((2, 0)\), we substitute \(x_1 = 0\), \(y_1=-2\), \(x_2 = 2\), \(y_2 = 0\) into the formula:
\(m=\frac{0 - (-2)}{2 - 0}=\frac{0 + 2}{2}=\frac{2}{2}=1\). So the slope of the graph is \(1\).

Step3: Determine the slope of the equation (assuming it's a linear equation)

For a linear equation in the form \(y = mx + b\), \(m\) is the slope. Since the graph is a straight line (linear), and we found the slope of the graph is \(1\), if the equation corresponds to this line, its slope should also be \(1\).

Step4: Compare the slopes

Since both the slope of the graph and the slope of the equation (assuming it's the equation of this line) are \(1\), they are the same.

Answer:

The slope of the graph is \(1\), the slope of the equation is \(1\), and yes, they have the same slopes.