Question

5-1 mathxl for school: practice & problem solving part 1 of 2 the points (18,21) and (30,35) 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 \( m=\frac{y_2 - y_1}{x_2 - x_1} \). Here, \( (x_1, y_1)=(18, 21) \) and \( (x_2, y_2)=(30, 35) \).

Step2: Substitute values into formula

Substitute \( x_1 = 18 \), \( y_1 = 21 \), \( x_2 = 30 \), \( y_2 = 35 \) into the slope formula: \( m=\frac{35 - 21}{30 - 18} \).

Step3: Simplify numerator and denominator

Calculate numerator: \( 35 - 21 = 14 \). Calculate denominator: \( 30 - 18 = 12 \). So, \( m=\frac{14}{12} \).

Step4: Reduce the fraction

Simplify \( \frac{14}{12} \) by dividing numerator and denominator by their greatest common divisor, which is 2. \( \frac{14\div2}{12\div2}=\frac{7}{6} \).

Answer:

\(\frac{7}{6}\)