Find the slope of the line which passes through the points A(0, -4) and B(8, 0).
Understand the Problem
The question is asking to find the slope of the line that passes through the points A(0, -4) and B(8, 0). This requires us to apply the formula for the slope between two points in a coordinate plane.
Answer
The slope is \( \frac{1}{2} \).
Answer for screen readers
The slope of the line passing through the points A(0, -4) and B(8, 0) is ( \frac{1}{2} ).
Steps to Solve
- Identify the coordinates of the points
The coordinates of points A and B are given as:
- ( A(0, -4) )
- ( B(8, 0) )
- Use the slope formula
The formula for the slope ( m ) of a line passing through two points ( (x_1, y_1) ) and ( (x_2, y_2) ) is: $$ m = \frac{y_2 - y_1}{x_2 - x_1} $$
- Substitute the coordinates into the slope formula
Substitute the coordinates into the formula:
- ( x_1 = 0 ), ( y_1 = -4 )
- ( x_2 = 8 ), ( y_2 = 0 )
Therefore: $$ m = \frac{0 - (-4)}{8 - 0} = \frac{0 + 4}{8} $$
- Calculate the slope
Now simplify the expression: $$ m = \frac{4}{8} = \frac{1}{2} $$
The slope of the line passing through the points A(0, -4) and B(8, 0) is ( \frac{1}{2} ).
More Information
The slope represents the rate of change of ( y ) with respect to ( x ). A slope of ( \frac{1}{2} ) indicates that for every 2 units you move horizontally to the right, the line rises vertically by 1 unit.
Tips
- Forgetting to subtract the ( y )-coordinates in the correct order. Always use ( y_2 - y_1 ).
- Confusing the ( x )-coordinates when substituting into the formula. Ensure to label which is ( x_1 ) and ( x_2 ).
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