Question

01 hw (2 pages)
for problems 1 and 2, plot the points on the axis and then find the slope between the two points.

1. (-1,4) and (2,6)
2. (-3,3) and (1,-5)

Explanation:

Problem 1: Points (-1, 4) and (2, 6)

Step 1: Recall the slope formula

The slope \( m \) between two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is given by \( m = \frac{y_2 - y_1}{x_2 - x_1} \).

Step 2: Identify the coordinates

Here, \( x_1 = -1 \), \( y_1 = 4 \), \( x_2 = 2 \), \( y_2 = 6 \).

Step 3: Substitute into the formula

\( m = \frac{6 - 4}{2 - (-1)} = \frac{2}{3} \).

Step 1: Recall the slope formula

The slope \( m \) between two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is \( m = \frac{y_2 - y_1}{x_2 - x_1} \).

Step 2: Identify the coordinates

Here, \( x_1 = -3 \), \( y_1 = 3 \), \( x_2 = 1 \), \( y_2 = -5 \).

Step 3: Substitute into the formula

\( m = \frac{-5 - 3}{1 - (-3)} = \frac{-8}{4} = -2 \).

Answer:

The slope between (-1, 4) and (2, 6) is \(\frac{2}{3}\).

Problem 2: Points (-3, 3) and (1, -5)