The function h(x) is graphed on the coordinate plane provided. Determine the statements that are true about the function h(x) . Select the two correct answers.
A line is graphed on a four quadrant coordinate plane. The x-axis and the y-axis go from negative 10 to 10 in increments of 1. The line passes through (negative 2, negative 5), and (4, negative 2).
Select the two correct answers.
(1 point)
Responses
The slope is 12
.
The slope is 1 half.
The y
-intercept is 12
.
The y-intercept is 1 half.
The x
-intercept is 4
.
The x-intercept is 4.
The slope is −2
.
The slope is negative 2.
The y
-intercept is −4
.
The two correct answers are:
-The slope is -2.
-The y-intercept is -4.
The two correct statements about the function h(x) are:
1. The slope is negative 2.
2. The x-intercept is 4.
To determine the statements that are true about the function h(x), we need to analyze the graph of the line passing through the given points (-2, -5) and (4, -2) on the coordinate plane.
1. Slope: The slope of a line can be found using the formula: slope = (change in y) / (change in x). Let's calculate it using the given points:
slope = (-2 - (-5)) / (4 - (-2))
= (-2 + 5) / (4 + 2)
= 3 / 6
= 1/2.
Therefore, the slope of the line is 1/2, indicating that the line is increasing but not very steep.
2. Y-intercept: To find the y-intercept, we observe the point where the line intersects the y-axis. In this case, the y-intercept is the y-coordinate when x = 0. Since we don't know this from the given points, we need to use the slope-intercept form of a line, which is y = mx + b, where m is the slope and b is the y-intercept. Rearranging the formula, we have b = y - mx.
Let's use the first given point (-2, -5) to find the y-intercept:
b = -5 - (1/2)(-2)
= -5 + 1
= -4.
Therefore, the y-intercept is -4.
Based on our calculations, the two correct statements about the function h(x) are:
- The slope is 1/2.
- The y-intercept is -4.