What are the intercepts of the function P(x) shown in the graph provided? 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 8 to 8 in increments of 0.5. The line passes through (negative 3, 0) and (3, negative 7).
Select the two correct answers.
(1 point)
Responses
y
-intercept: −3
y-intercept: negative 3
x
-intercept: −72
x-intercept: negative 7 halves
y
-intercept: −72
y-intercept: negative 7 halves
x
-intercept: 3
x-intercept: 3
x
-intercept: −3
x-intercept: negative 3
The intercepts of a function are the x and y values where the graph intersects the x and y axes, respectively.
From the graph, we can see that the line passes through the point (-3, 0) and (3, -7).
Therefore, the y-intercept is -3 and the x-intercept is 3.
The correct answers are:
y-intercept: -3
x-intercept: 3
To find the intercepts of the function P(x) shown in the graph provided, we need to identify the points where the graph intersects the x-axis and the y-axis.
From the graph, we can see that the line passes through the points (-3, 0) and (3, -7).
To find the x-intercept, we need to find the value of x when y = 0 (on the x-axis). From the given points, we can see that the point (-3, 0) lies on the x-axis. Therefore, the x-intercept is -3.
To find the y-intercept, we need to find the value of y when x = 0 (on the y-axis). From the given points, we can see that the point (0, -7) lies on the y-axis. Therefore, the y-intercept is -7.
So, the correct answers are:
- x-intercept: -3
- y-intercept: -7
To find the intercepts of a function from a graph, we need to identify the points where the graph intersects the x-axis and the y-axis.
From the given graph, we can see that the line passes through the points (-3, 0) and (3, -7).
The x-intercept is the point where the line intersects the x-axis, meaning the y-coordinate is 0. So, the x-intercept is the point (-3, 0).
The y-intercept is the point where the line intersects the y-axis, meaning the x-coordinate is 0. However, we don't have the coordinates of the point where the line intersects the y-axis directly from the graph. But we can find it by substituting x = 0 into the equation of the line.
First, we find the equation of the line using the given points (-3, 0) and (3, -7) using the slope-intercept form: y = mx + b, where m is the slope and b is the y-intercept.
We can find the slope (m) using the formula: m = (change in y)/(change in x) = (-7 - 0)/(3 - (-3)) = -7/6.
Using the slope-intercept form, we have y = (-7/6)x + b. We can substitute one of the given points, let's use (-3, 0), into the equation to solve for b.
0 = (-7/6)(-3) + b
0 = 7/2 + b
b = -7/2.
Therefore, the equation of the line is y = (-7/6)x - 7/2.
Now, substituting x = 0 into the equation, we can find the y-intercept.
y = (-7/6)(0) - 7/2
y = -7/2.
So, the y-intercept is the point (0, -7/2).
Therefore, the correct answers are:
1) x-intercept: -3
2) y-intercept: -7/2