3C Linear Features & 2C Write Linear Equation From Graph

​3C: graph linear functions on the coordinate plane and identify key features, including x-intercept, y-intercept, zeros, and slope

​Linear Function: y = mx + b OR f(x) = mx + b
where m represents slope of the line and
b represents the y-intercept of the line

​y = -5x + 5

​SLOPE: steepness and direction of a straight line

​ Positive Slope

​COUNT EACH BOX FROM ONE
POINT STRAIGHT UP TO ANOTHER
POINT. THEN COUNT EACH BOX
FROM ONE POINT TO ANOTHER POINT TO THE RIGHT.

​COUNT EACH BOX FROM ONE
POINT STRAIGHT DOWN TO ANOTHER POINT. THEN COUNT EACH BOX FROM ONE POINT TO ANOTHER POINT TO THE RIGHT.

​HORIZONTAL LINE WITH
AN EQUATION
Y = Y-INTERCEPT.

​VERTICAL LINE WITH
AN EQUATION
X = X-INTERCEPT.

​ Negative Slope

​ Zero Slope

​ Undefined Slope

​Y-INTERCEPT: point where the graph crosses the y-axis; y-value when x = 0. Written as (0, y-value)

​X-INTERCEPT: point where the graph crosses the x-axis; x-value when y = 0. Written as (x-value, 0).
ALSO called zeros or solutions.

​x-intercept: (5, 0)

​y-intercept: (0, -1)

Multiple Choice

Linear function t has an x-intercept of -1 and a y-intercept of 5.

Which graph best represents t ?

Math Response

The graph of linear function, f, is shown.

What is the zero of f ?

Type answer here

Correct Answer: 2

Deg^°

Rad

Drag and Drop

The graph of a linear function is shown on the grid.

The x-intercept of the line is ​

Placeholder

.

The y-intercept of the line is ​

Placeholder

.

Drag these tiles and drop them in the correct blank above

(-2, 0)

(0, 8)

(0, -2)

(8, 0)

(2, 0)

(0, 2)

(-8, 0)

(0, -8)

Multiple Choice

Linear function k has a zero of -2 and a y-intercept of 6.

Which graph best represents k ?

Drag and Drop

The graph of linear function g passes through the points (-7, -4) and (7, 6) as shown.

The slope of the graph of g is ​

Placeholder

.

The y-intercept of the graph of g is ​

Placeholder

.

Drag these tiles and drop them in the correct blank above

1

-1

-1.5

Dropdown

The graph models the linear relationship between the number of monthly payments made on a loan and the remaining balance in dollars left to pay on the loan.

Complete the statement to best describe the x-intercept of the graph.



The x-intercept is ​

Select answer

, which represents the ​

Select answer

.​

Math Response

The graph of linear function f passes through the point (1, -9) and has a slope of -3.

What is the zero of f ?

Type answer here

Correct Answer: -2

Deg^°

Rad

Multiple Choice

The water level of a river was measured each day during a two-week period. The graph models the linear relationship between the water level of the river in feet and the number of days the water level was measured.

Which statement best describes the y-intercept of the graph?

• The water level increased by 0.25 ft per day.

• The maximum water level was 19.5 ft.

• The initial water level was 16 ft.

• The water level was measured for 14 days.

Math Response

A paper airplane was thrown from the top of a tall building. The height of the paper airplane above the ground can be found using the function y = -1.5x + 60, where x is the time in seconds that the paper airplane has been in the air.

How many seconds did it take the paper airplane to reach the ground?

HINT: what is the x-intercept (graph the function)

Type answer here

Correct Answer: 40

Deg^°

Rad

Multiple Choice

Which line appears to have an x-intercept of -5 and a y-intercept of 3 ?

Dropdown

The graph of a function is shown on the grid.

The location of the y-intercept is at (​

Select answer

, ​

Select answer

).

Math Response

The graph of linear function g is shown on the grid.

What is the zero of g ?

Type answer here

Correct Answer: -6

Deg^°

Rad

Multiple Choice

What is the y-intercept of the line graphed on the grid?

• (0, 5.5)

• (0, 7.5)

• (5.5, 0)

• (7.5, 0)

Multiple Choice

Which graph shows a line with an x-intercept of -5?

Drag and Drop

The graph of a linear function is shown on the grid.

The equation best represented by this graph is

y = ​

Placeholder

x + ​

Placeholder

Drag these tiles and drop them in the correct blank above

7

-7

Multiple Choice

The conversion of degrees Celsius to degrees Fahrenheit can be represented by a linear relationship. The graph shows the linear relationship between y, the temperature in degrees Fahrenheit, and x, the temperature in degrees Celsius from the freezing point of water.

Which equation best represents this situation?

• $$y=\frac{5}{9}x$$

• $$y=\frac{9}{5}x$$

• $$y=\frac{5}{9}x+32$$

• $$y=\frac{9}{5}x+32$$

Dropdown

The graph of a linear function is shown on the grid.

Choose from the drop-down menus to write the function that best represents this graph.

y = ​

Select answer

x + ​

Select answer