Question

the points (-2, r) and (10, 1) lie on a line with slope $-\frac{3}{4}$. find the missing coordinate r.

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, \( (x_1,y_1)=(-2,r) \), \( (x_2,y_2)=(10,1) \), and \( m = -\frac{3}{4} \).

Step2: Substitute into slope formula

Substitute the values into the formula: \( -\frac{3}{4}=\frac{1 - r}{10 - (-2)} \). Simplify the denominator: \( 10 - (-2)=12 \), so we have \( -\frac{3}{4}=\frac{1 - r}{12} \).

Step3: Solve for \( r \)

Multiply both sides by 12: \( 12\times(-\frac{3}{4})=1 - r \). Calculate left side: \( -9 = 1 - r \). Subtract 1 from both sides: \( -9 - 1=-r \), so \( -10=-r \). Multiply both sides by -1: \( r = 10 \).

Answer:

\( r = 10 \)