The points (p, -4) and (0, 6) fall on a line with a slope of 10/7. What is the value of p?
Understand the Problem
The question involves finding the value of p in the coordinate point (p, -4) such that the slope between the points (p, -4) and (0, 6) equals 10/7. The slope formula will be applied to solve for p.
Answer
The value of \( p \) is \( -7 \).
Answer for screen readers
The value of ( p ) is ( -7 ).
Steps to Solve
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Identify the points and slope The points given are ((p, -4)) and ((0, 6)). The slope ( m ) is given as ( \frac{10}{7} ).
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Use the slope formula The slope ( m ) between two points ((x_1, y_1)) and ((x_2, y_2)) is defined as: $$ m = \frac{y_2 - y_1}{x_2 - x_1} $$ Substituting the known values: $$ \frac{10}{7} = \frac{6 - (-4)}{0 - p} $$
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Simplifying the equation Calculate the difference in the numerator: $$ 6 - (-4) = 6 + 4 = 10 $$ So now the equation is: $$ \frac{10}{7} = \frac{10}{0 - p} $$
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Cross-multiply to solve for p Cross-multiplying gives us: $$ 10(0 - p) = 7 \times 10 $$ Expanding and simplifying leads to: $$ -10p = 70 $$
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Solve for p To find ( p ), divide both sides by -10: $$ p = -\frac{70}{10} $$ $$ p = -7 $$
The value of ( p ) is ( -7 ).
More Information
In this problem, we learned how to find a missing coordinate using the slope formula. Slope is a measure of how steep a line is, calculated using the rise over run between two points.
Tips
- Not correctly substituting values into the slope formula.
- Forgetting to simplify the equation before solving for ( p ).
- Neglecting the negative sign when working with negative coordinates.
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