Question

1. find the value of x so that the line through the points (1, 12) and (x, 27) have a slope of \\(\frac{3}{2}\\). (3 points)

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, \((x_1,y_1)=(1,12)\), \((x_2,y_2)=(x,27)\), and \( m = \frac{3}{2} \).

Step2: Substitute into formula

Substitute the values into the slope formula: \(\frac{3}{2}=\frac{27 - 12}{x - 1}\).

Step3: Simplify numerator

Simplify the numerator: \(27 - 12 = 15\), so the equation becomes \(\frac{3}{2}=\frac{15}{x - 1}\).

Step4: Cross - multiply

Cross - multiply: \(3(x - 1)=2\times15\).

Step5: Expand and solve

Expand the left side: \(3x-3 = 30\). Add 3 to both sides: \(3x=30 + 3=33\). Divide both sides by 3: \(x=\frac{33}{3}=11\).

Answer:

\(x = 11\)