What is the slope, m, and y-intercept for the line that is plotted on the grid below?
On a coordinate plane, a line goes through points (0, 4) and (negative 2, 0).
m = One-half, (0, –2)
m = One-half, (0, 4)
m = 2, (0, –2)
m = 2, (0, 4)
The correct answer is m = One-half, (0, –2)
To find the slope (m) and y-intercept of a line, we can use the formula:
m = Δy / Δx
where Δy represents the change in y-coordinates and Δx represents the change in x-coordinates between two points on the line.
Let's use this formula to find the slope and y-intercept for the line that goes through the points (0, 4) and (-2, 0).
First, let's calculate the change in y (Δy) and change in x (Δx):
Δy = 0 - 4 = -4
Δx = -2 - 0 = -2
Now, we can substitute these values into the slope formula:
m = (-4) / (-2) = 2
Therefore, the slope (m) for the line is 2.
To find the y-intercept, we can use the equation of a straight line:
y = mx + b
where m is the slope and b is the y-intercept.
We already found that m = 2. Let's use one of the given points, (0, 4), to solve for the y-intercept (b):
4 = (2)(0) + b
Since anything multiplied by zero is zero, the equation simplifies to:
4 = b
Therefore, the y-intercept (b) for the line is 4.
So, the slope (m) is 2, and the y-intercept is 4 for the line plotted on the grid.