What are the slope and the y-intercept of the linear function that is represented by the graph?
On a coordinate plane, a line goes through points (0, negative 2) and (3, 0).
The slope is Two-thirds, and the y-intercept is –2.
The slope is Two-thirds, and the y-intercept is 3.
The slope is Three-halves, and the y-intercept is –2.
The slope is Three-halves, and the y-intercept is 3.
To find the slope and y-intercept of a linear function represented by a graph, we need to use the coordinates of two points on the line. Let's use the given points (0, -2) and (3, 0) to find the slope and y-intercept.
1. Slope (m): The slope of a line can be found using the formula:
m = (y2 - y1) / (x2 - x1)
Let's substitute the coordinates (x1, y1) = (0, -2) and (x2, y2) = (3, 0) into the formula:
m = (0 - (-2)) / (3 - 0)
= 2 / 3
Therefore, the slope of the line is 2/3.
2. Y-intercept (b): The y-intercept is the value of y when x = 0. By looking at the graph, we can see that the line intersects the y-axis at y = -2. So, the y-intercept is -2.
Therefore, based on the given options, the correct answer is:
The slope is Two-thirds, and the y-intercept is –2.
The slope and y-intercept of the linear function represented by the graph are:
The slope is Two-thirds, and the y-intercept is –2.
the slope m = (0+2)/(3-0) = 2/3
The y-intercept is where x=0