Question

Calculate the rate of change (slope)
for the given line.
20
2
о

Answer 1

Slope is equal to -3/2.

Explanation:

Finds two points on an exact point. For the case of demonstration, I'll use (2, -2) and (0, 1).

Now, you can either use a formula, or do the rise-over-run method. For the formula, it would be (y2 - y1) / (x2 - x1) = slope.

For this example, the equation would be (1 - (-2) / (0 - 2). Cancel out the negatives in the numerator, and you'd get (3) / (-2). This is equivalent to -3/2.

For the rise over run method, you count how many units it goes down and over. Using the same points, to get from one to the other, you need to go down three units and to the right to. Since we're decreasing, the three is negative. The "rise," or whatever increase/decrease it is, will go in the numerator, while the "run" will go in the denominator.

This would also get you -3/2. Ask your teacher whether or not they're fine with the rise-over-run method, because a few teachers require algebraic use.

Answer 2

`\sf slope =(-3)/(2)`

Explanation:

To find the slope, mark any two point on the line.

(-2, 4) ; (2 , -2)

`\sf x_1 = -2 ; \ y_1 = 4 \\\\x_2 = 2 ; \ y_2 = -2 \\\\ \boxed{\bf Slope = (y_2-y_1)/(x_2-x_1)}`

`\sf = (-2-4)/(2-[-2])\\\\=(-6)/(2+2)\\\\=(-6)/(4)\\\\=(-3)/(2)`