Question

the points (7,8) and (49,56) form a proportional relationship. find the slope of the line through the points. then use the slope to graph the line. the slope is \boxed{}. (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

Let \((x_1, y_1)=(7, 8)\) and \((x_2, y_2)=(49, 56)\).

Step3: Substitute into formula

Substitute the values into the slope formula: \( m=\frac{56 - 8}{49 - 7} \).

Step4: Simplify numerator and denominator

Simplify the numerator: \( 56 - 8 = 48 \).
Simplify the denominator: \( 49 - 7 = 42 \).
So, \( m=\frac{48}{42} \).

Step5: Reduce the fraction

Divide numerator and denominator by their greatest common divisor, which is 6. \( \frac{48\div6}{42\div6}=\frac{8}{7} \).

Answer:

\(\frac{8}{7}\)