Linear Functions Vocabulary

Which of the following is NOT a solution to the equation x - y = 5? a. (4, -1) b. (9, 4) c. (0, 5) d. (8, 3)

(0, 5)

Which of the following points are y-intercepts? Select all that apply. a. (0, 9) b. (-7, 0) c. (0, -3) d. (2, 0)

(0, 9) and (0, -3)

The rise is found by subtracting y-values

(x1, y1) (x2, y2) rise = y2 - y1

The run is found by subtracting x-values

(x1, y1) (x2, y2) run = x2 - x1

On a graph, the slope measures the steepness of a line

- A line with a positive slope goes up from left to right. - A line with a negative slope goes down from left to right.

Consider the ordered pairs (3, -2), (-1, 5), and (-9, -8). Which of the following is NOT an x-coordinate? a. -8 b. 3 c. -1 d. -9

-8

(0, 0)

Find the solution.

Graphing vertical lines

If an equation may be written in the form x = a, where a is a real number, then the graph of the equation is a vertical line; that is, it is a straight line that is parallel to the y-axis

Graphing horizontal lines

If an equation may be written in the form y = b, where b is a real number, then the graph of the equation is a horizontal line; that is, it is a straight line that is parallel to the x-axis

Which of the following does NOT describe the x-intercept of a line? a. The x-intercept of a line is the point where the line crosses the x-axis. b. The x-intercept of a line is found by letting x = 0 and solving for y. c. If a linear equation has an x-intercept, it can be one of the points used to graph a line. d. The x-intercept of a line is an ordered pair with the coordinates (a, 0), where a is a real number.

The x-intercept of a line is found by letting x = 0 and solving for y.

What is the slope of a vertical line?

Undefined.

y = -2x + 3

What is the equation of the line shown?

y = 3x - 2

What is the equation of the line shown?

Which of the following best describes the slope m of a line? a. m = run / rise b. slope = change in x-coordinates / change in y-coordinates c. m = y / x d. m = rise / run

m = rise / run

The m in the y=mx+b is the

slope of the line

Intercept

the point at which a line crosses an axis is called an intercept.

On the x-axis

the positive direction is to the right and the negative direction is to the left.

On the y-axis

the positive direction is up and the negative direction is down.

Slope

the rate of change between two ordered pair solutions to a linear equation is called a slope. The variable m is typically used to represent slope.

Rise

the rise of a line is the change in the vertical position, or the difference between the y-coordinates of two points on the line.

Run

the run of a line is the change in the horizontal position, or the difference between the x-coordinates of two points on the line.

x-Intercept

the x-intercept of a line is the point where the line crosses the x-axis. The x-intercept is an ordered pair with the coordinates (a, 0), where a is a real number.

b

the y-intercept

y-Intercept

the y-intercept of a line is the point where the line crosses the y-axis. The y-intercept is an ordered pair with the coordinates (o, b), where b is a real number.

To graph a linear equation in two variables:

1.) Find three ordered pairs that are solutions to the linear equation. 2.) Plot the ordered pairs on the graph. 3.) Draw a line through the three points.

Finding the y-intercept of a linear equation:

1.) Let x = 0 2.) Solve for y

Finding the x-intercept of a linear equation:

1.) Let y = 0 2.) Solve for x

To find a solution to a linear equation in two variables:

1.) Substitute a value for one of the variables. 2.) Solve the equation to find the value of the other variable.

Is (3, 5) a solution to 3x + 2y = 19?

3(3) + 2(5) = 19 9 + 10 = 19 19 = 19 TRUE

Is (6, -4) a solution to 3x = 2y + 10?

3(6) = 2(-4) + 10 18 = -8 + 10 18 = 2 FALSE

Which of the following equations shows an INCORRECT substitution of the ordered pair (3, 5)? a. -2x - y = 0 -2(3) - 5 = 0 b. 9x = y + 2 9(3) = 5 + 2 c. 3y = 2x + 1 3(3) = 2(5) + 1 d. -4 = 9y + 3x -4 = 9(5) + 3(3)

3y = 2x + 1 3(3) = 2(5) + 1

Most linear equations have one x-intercept and one y-intercept.

Some linear equations only have one intercept.

Which is the correct process for plotting the ordered pair (-2, -1)? a. Start at the origin, move two units to the right, and then move up one unit. b. Start at the origin, move two units down, and then move one unit to the left. c. Start at the origin, move two units to the left, and then move down one unit. d. Start at the origin, move one unit down, and then move two units to the right.

Start at the origin, move two units to the left, and then move down one unit.

x-Coordinate

is the first number in an ordered pair and it represents the location relative to the x-axis.

What is the slope of a horizontal line?

Zero.

y-Coordinate

is the second number in an ordered pair and it represents the location relative to the y-axis.

Ordered Pair

is a solution in an equation if it results in a true statement when the values for the x-coordinate and the y-coordinate are substituted into the equation.

Origin

is represented by the ordered pair (0, 0), and it has both x- and y-coordinates of 0.

Which of the following does NOT appear on a blank graph or in the definition of the rectangular coordinate system? a. ordered pair b. y-axis c. origin d. x-axis

ordered pair

Choose the equation that will be a horizontal line when graphed. a. y = 2 b. x - y = 0 c. x = 4 d. y = 5x

y = 2

Which of the following is the slope-intercept form of a line? a. y = bx + m b. m = y2 - y1 / x2 - x1 c. Ax + By = C d. y = mx + b

y = mx + b

The b in y=mx+b is the

y-intercept (where the line crosses the y-axis)

Slope-intercept form for equation of a line.

y=mx+b