Find the slope of the line passing through the points (-8, -3) and (-3, 4).
Understand the Problem
The question asks to find the slope of a line given two points on the line. The slope can be calculated using the formula: slope = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the two points.
Answer
$\frac{7}{5}$
Answer for screen readers
$\frac{7}{5}$
Steps to Solve
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Identify the coordinates We are given the two points: (-8, -3) and (-3, 4). Let's label them: $x_1 = -8$, $y_1 = -3$ $x_2 = -3$, $y_2 = 4$
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Apply the slope formula The slope formula is: $m = \frac{y_2 - y_1}{x_2 - x_1}$
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Substitute the values Substitute the coordinates into the slope formula: $m = \frac{4 - (-3)}{-3 - (-8)}$
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Simplify the expression Simplify the numerator and the denominator: $m = \frac{4 + 3}{-3 + 8}$ $m = \frac{7}{5}$
$\frac{7}{5}$
More Information
The slope of the line passing through the points (-8, -3) and (-3, 4) is $\frac{7}{5}$. This means that for every 5 units you move to the right on the line, you move 7 units up.
Tips
A common mistake is to mix up the coordinates in the slope formula, such as calculating (x2 - x1) / (y2 - y1) instead of (y2 - y1) / (x2 - x1), or incorrectly substituting the negative signs, especially when subtracting a negative number. It is also important to consistently use the same order of points in both the numerator and denominator.
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