Find the slope of the line passing through the points (-3, 3) and (5, 9).
Understand the Problem
The question is asking to find the slope of a line that connects two given points, which is a common problem in coordinate geometry.
Answer
The slope is \( \frac{3}{4} \).
Answer for screen readers
The slope of the line passing through the points ( (-3, 3) ) and ( (5, 9) ) is ( \frac{3}{4} ).
Steps to Solve
- Identify the given points
The points provided are ( (-3, 3) ) and ( (5, 9) ).
- Use the slope formula
The slope ( m ) of a line passing through two points ( (x_1, y_1) ) and ( (x_2, y_2) ) is calculated using the formula:
$$ m = \frac{y_2 - y_1}{x_2 - x_1} $$
- Plug in the coordinates
Substitute the coordinates of the points into the slope formula:
Let ( (x_1, y_1) = (-3, 3) ) and ( (x_2, y_2) = (5, 9) ):
$$ m = \frac{9 - 3}{5 - (-3)} $$
- Calculate the differences
Perform the subtraction:
$$ m = \frac{6}{5 + 3} $$
This simplifies to:
$$ m = \frac{6}{8} $$
- Simplify the fraction
Now simplify ( \frac{6}{8} ):
$$ m = \frac{3}{4} $$
The slope of the line passing through the points ( (-3, 3) ) and ( (5, 9) ) is ( \frac{3}{4} ).
More Information
The slope indicates how steep the line is. A slope of ( \frac{3}{4} ) means that for every 4 units moved horizontally, the line rises by 3 units. This shows a positive relationship between the x and y coordinates.
Tips
- Confusing the order of points; ensure to use the correct coordinates in the formula.
- Forgetting to simplify the fraction after calculating the slope.
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