What is the slope of the line that passes through the points (-4, 2) and (5, 9)?
Understand the Problem
The question is asking for the slope of the line that passes through the two given points: (-4, 2) and (5, 9). To find the slope, we use the formula (y2 - y1) / (x2 - x1) where (x1, y1) and (x2, y2) are the coordinates of the points.
Answer
The slope of the line is \( \frac{7}{9} \).
Answer for screen readers
The slope of the line is ( m = \frac{7}{9} ).
Steps to Solve
-
Identify the points The given points are ( (x_1, y_1) = (-4, 2) ) and ( (x_2, y_2) = (5, 9) ).
-
Use the slope formula To find the slope ( m ), use the formula:
$$ m = \frac{y_2 - y_1}{x_2 - x_1} $$
- Substitute the values Substituting the coordinates into the formula, we get:
$$ m = \frac{9 - 2}{5 - (-4)} $$
- Simplify the numerator and denominator Calculate:
- Numerator: ( 9 - 2 = 7 )
- Denominator: ( 5 + 4 = 9 )
So the slope becomes:
$$ m = \frac{7}{9} $$
- Final answer The slope of the line that passes through the points is ( \frac{7}{9} ).
The slope of the line is ( m = \frac{7}{9} ).
More Information
The slope represents the steepness of the line and is a measure of how much ( y ) increases for a unit increase in ( x ). In this case, for every 9 units you move in the ( x )-direction, the line moves up 7 units in the ( y )-direction.
Tips
- Confusing the order of the points can lead to an incorrect slope. Always ensure you use the coordinates correctly in the formula.
- Neglecting to subtract correctly can result in calculation errors.
AI-generated content may contain errors. Please verify critical information
