Question

a line with a slope of $-\frac{9}{10}$ passes through the points $(h, -7)$ and $(-9, 2)$. what is the value of $h$?
$h = \square$
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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, \( m = -\frac{9}{10} \), \( (x_1, y_1)=(h, - 7) \), \( (x_2, y_2)=(-9,2) \). So we substitute into the formula:
\( -\frac{9}{10}=\frac{2 - (-7)}{-9 - h} \)

Step2: Simplify numerator

Simplify the numerator \( 2-(-7)=2 + 7 = 9 \). So the equation becomes:
\( -\frac{9}{10}=\frac{9}{-9 - h} \)

Step3: Cross - multiply

Cross - multiply to get \( -9\times(-9 - h)=10\times9 \)

Step4: Expand left - hand side

Expand the left - hand side: \( 81+9h = 90 \)

Step5: Solve for h

Subtract 81 from both sides: \( 9h=90 - 81=9 \)
Then divide both sides by 9: \( h = 1 \)

Answer:

\( h = 1 \)