What is the slope of the line through (1,0) and (3,8)?
Choose 1 answer:
A)1/4
B)4
C)-1/4
D)-4
The Correct Answer and Explanation is :
The correct answer is: B) 4
To find the slope of a line through two points, we can use the formula for slope, given by:
[
m = \frac{y_2 – y_1}{x_2 – x_1}
]
where ((x_1, y_1)) and ((x_2, y_2)) are the coordinates of the two points. In this case, we have the points ((1, 0)) and ((3, 8)).
- Assign the coordinates:
- Let ((x_1, y_1) = (1, 0))
- Let ((x_2, y_2) = (3, 8))
- Substitute into the slope formula:
- First, find (y_2 – y_1):
[
y_2 – y_1 = 8 – 0 = 8
] - Next, find (x_2 – x_1):
[
x_2 – x_1 = 3 – 1 = 2
] - Now, substitute these values into the slope formula:
[
m = \frac{y_2 – y_1}{x_2 – x_1} = \frac{8}{2} = 4
]
Therefore, the slope of the line through the points ((1, 0)) and ((3, 8)) is (4).
Explanation of the Result
The slope of a line represents how steep the line is, indicating the rate of change in the (y)-coordinate for each unit change in the (x)-coordinate. A positive slope, like (4), indicates that as (x) increases, (y) also increases, meaning the line rises as it moves from left to right.
In this scenario, for every unit increase in (x) (the horizontal distance), (y) increases by (4) units (the vertical distance). This steepness indicates a relatively rapid increase in (y) compared to the increase in (x).
Understanding slope is crucial in various fields such as physics, engineering, and economics, where it can represent rates of change, trends, and predictions. In graphical representations, a slope of (4) means the line rises significantly, indicating a strong positive correlation between the variables represented by (x) and (y).
Thus, the correct answer is B) 4.