Question

part 1 of 2
the points (4,5) and (12,15) form a proportional relationship. find the slope of the line through the points. then use the slope to graph the line.
the slope is
(simplify your answer.)

Explanation:

Step1: Recall slope formula

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

Step2: Identify coordinates

Here, \( x_1 = 4 \), \( y_1 = 5 \), \( x_2 = 12 \), \( y_2 = 15 \).

Step3: Substitute into formula

Substitute the values into the slope formula: \( m=\frac{15 - 5}{12 - 4} \).

Step4: Simplify the expression

Simplify the numerator and denominator: \( 15 - 5 = 10 \) and \( 12 - 4 = 8 \), so \( m=\frac{10}{8} \). Then simplify the fraction: \( \frac{10}{8}=\frac{5}{4} \).

Answer:

\(\frac{5}{4}\)