To find the rate of change (slope), we need to use the formula:
m = (y2 - y1)/(x2 - x1)
Using the values from the table:
m = (8 - 4)/(-3 - 1) = 4/-4 = -1
So, the rate of change is m = -1.
To find the initial value (y-intercept), we can choose any point from the table. Let's use the point (1, 4).
Using the point-slope formula:
y = mx + b
Substitute in the values:
4 = -1(1) + b
4 = -1 + b
b = 4 + 1
b = 5
Therefore, the initial value (y-intercept) is b = 5.
Slope and y-intercepts Practice
Complete this assessment to review what you've learned. It will not count toward your grade.
3 of 53 of 5 Items
Question
Use the table to answer the question.
x y
1 4
−3 8
Find the rate of change and the initial value of the linear function given as a table of values.
(1 point)
The rate of change is m=
, and the initial value is b=???
.
5 answers
Use the image to answer the question.
An illustration of a coordinate plane with four quadrants shows the x and y axes extending from negative 5 to 5 in increments of 1. An upward slanting line is plotted on the coordinate plane. The upward slanting line with arrows on both ends passes through the following closed points: left parenthesis 0 comma 0 right parenthesis and left parenthesis 2 comma 3 right parenthesis.
Determine the initial value and the rate of change of the linear function given in the graph.
(1 point)
The initial value is
, and the rate of change is
.
An illustration of a coordinate plane with four quadrants shows the x and y axes extending from negative 5 to 5 in increments of 1. An upward slanting line is plotted on the coordinate plane. The upward slanting line with arrows on both ends passes through the following closed points: left parenthesis 0 comma 0 right parenthesis and left parenthesis 2 comma 3 right parenthesis.
Determine the initial value and the rate of change of the linear function given in the graph.
(1 point)
The initial value is
, and the rate of change is
.
To determine the initial value and rate of change from the graph, we can use the two points that are plotted: (0, 0) and (2, 3).
To find the rate of change (slope), we use the formula:
m = (y2 - y1)/(x2 - x1)
Using the points (0, 0) and (2, 3):
m = (3 - 0)/(2 - 0) = 3/2 = 1.5
So, the rate of change is m = 1.5.
To find the initial value (y-intercept), we can use the point (0, 0).
Therefore, the initial value of the linear function is b = 0.
Therefore, the initial value is b = 0, and the rate of change is 1.5.
To find the rate of change (slope), we use the formula:
m = (y2 - y1)/(x2 - x1)
Using the points (0, 0) and (2, 3):
m = (3 - 0)/(2 - 0) = 3/2 = 1.5
So, the rate of change is m = 1.5.
To find the initial value (y-intercept), we can use the point (0, 0).
Therefore, the initial value of the linear function is b = 0.
Therefore, the initial value is b = 0, and the rate of change is 1.5.
Slope and y-intercepts Practice
Complete this assessment to review what you've learned. It will not count toward your grade.
5 of 55 of 5 Items
Question
Use the image to answer the question.
An illustration of a coordinate plane with four quadrants shows the x and y axes extending from negative 5 to 5 in increments of 1. A downward slanting line is plotted on the coordinate plane. The downward slanting line with arrows on both ends passes through the following closed points: left parenthesis negative 3 comma 2.5 right parenthesis, left parenthesis 0 comma 1 right parenthesis, and left parenthesis 2 comma 0 right parenthesis.
Determine the initial value and the rate of change of the linear function as given in the graph.
(1 point)
The initial value is
, and the rate of change is
.
Complete this assessment to review what you've learned. It will not count toward your grade.
5 of 55 of 5 Items
Question
Use the image to answer the question.
An illustration of a coordinate plane with four quadrants shows the x and y axes extending from negative 5 to 5 in increments of 1. A downward slanting line is plotted on the coordinate plane. The downward slanting line with arrows on both ends passes through the following closed points: left parenthesis negative 3 comma 2.5 right parenthesis, left parenthesis 0 comma 1 right parenthesis, and left parenthesis 2 comma 0 right parenthesis.
Determine the initial value and the rate of change of the linear function as given in the graph.
(1 point)
The initial value is
, and the rate of change is
.
To determine the initial value and rate of change from the graph given, we can use the three points that are plotted: (-3, 2.5), (0, 1), and (2, 0).
To find the rate of change (slope), we can calculate it using the formula:
m = (y2 - y1) / (x2 - x1)
Let's use the points (0, 1) and (-3, 2.5) to find the rate of change:
m = (1 - 2.5) / (0 - (-3))
m = -1.5 / 3
m = -0.5
So, the rate of change is m = -0.5.
To find the initial value (y-intercept), we can use any of the points. Let's use (0, 1).
Therefore, the initial value of the linear function given in the graph is b = 1.
Therefore, the initial value is b = 1, and the rate of change is -0.5.
To find the rate of change (slope), we can calculate it using the formula:
m = (y2 - y1) / (x2 - x1)
Let's use the points (0, 1) and (-3, 2.5) to find the rate of change:
m = (1 - 2.5) / (0 - (-3))
m = -1.5 / 3
m = -0.5
So, the rate of change is m = -0.5.
To find the initial value (y-intercept), we can use any of the points. Let's use (0, 1).
Therefore, the initial value of the linear function given in the graph is b = 1.
Therefore, the initial value is b = 1, and the rate of change is -0.5.
5 answers