Question

a line that includes the points (j, -6) and (-7, 1) has a slope of $-\frac{7}{9}$. what is the value of j?
j =
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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, \( (x_1,y_1)=(j, - 6) \), \( (x_2,y_2)=(-7,1) \), and \( m =-\frac{7}{9} \). So we substitute into the formula: \(-\frac{7}{9}=\frac{1-(-6)}{-7 - j}\)

Step2: Simplify the numerator

Simplify \( 1-(-6) \) to get \( 1 + 6=7 \). So the equation becomes \(-\frac{7}{9}=\frac{7}{-7 - j}\)

Step3: Cross - multiply

Cross - multiply to get \(-7\times(-7 - j)=7\times9\)

Step4: Simplify both sides

Left side: \( 49+7j \), Right side: \( 63 \). So \( 49 + 7j=63 \)

Step5: Solve for j

Subtract 49 from both sides: \( 7j=63 - 49=14 \). Then divide both sides by 7: \( j=\frac{14}{7}=2 \)

Answer:

\( j = 2 \)