Question

1. through (2, 0) and (4, 4)

which shows the correct way to find the slope?
\frac{0 - 4}{4 - 2}
\frac{4 - 0}{4 - 2}
\frac{0 - 4}{2 - 4}
4 through (5, 1) and (-5, -3)

Explanation:

Step1: Recall slope formula

The slope \( m \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is \( m=\frac{y_2 - y_1}{x_2 - x_1} \). Here, the points are \((2, 0)\) (so \( x_1 = 2, y_1 = 0 \)) and \((4, 4)\) (so \( x_2 = 4, y_2 = 4 \)).

Step2: Substitute into formula

Substitute \( y_2 = 4, y_1 = 0, x_2 = 4, x_1 = 2 \) into the slope formula: \( m=\frac{4 - 0}{4 - 2} \). Now check the options:

• First option: \( \frac{0 - 4}{4 - 2} \) (incorrect, numerator is \( y_1 - y_2 \) instead of \( y_2 - y_1 \))
• Second option: \( \frac{4 - 0}{4 - 2} \) (matches our calculation)
• Third option: \( \frac{0 - 4}{2 - 4} \) (incorrect, denominator is \( x_1 - x_2 \) and numerator is \( y_1 - y_2 \))

Answer:

B. \( \frac{4 - 0}{4 - 2} \) (assuming the second option is labeled as B, with the expression \( \frac{4 - 0}{4 - 2} \))