Study Guides | linear functions | 8-5-3. Linear Functions

Study Guide: 8-5-3. Linear Functions

Vocabulary

Term  Description
Cartesian Plane a two-dimensional plane divided into four quadrants using x- and y-axis
Origin the point of intersection of the x-axis and y-axis on a Cartesian Plane
Function a relationship between variables that has one output for each and every input
Linear Function a function that is represented by a line when graphed on a Cartesian Plane
Domain the set of input values or x-values of a function
Range the set of output values or y-values of a function
Slope a ratio of the rate at which the dependent variable is changing versus the rate at which the independent variable is changing; frequently expressed as $\frac{RISE}{RUN}$, or $\frac{\textit{The change in y}}{\textit{The change in x}}$
Slope-Intercept form the form $y = mx + b$ of a linear equation, where m represents the slope of the line and b represents its y-intercept
Point-Slope form the form $y - y_1 = m(x - x_1)$ of a linear equation, where m is the slope, and $y_1$ and $x_1$ are the coordinates of a point.
x-intercept the point on the x-axis where the line of a function crosses the x-axis
y-intercept the point on the y-axis where the line a function crosses the y-axis
Absolute Value the distance a number is from zero on a number line (distance is never negative)

 

 

Questions

  1. Which point is on the y-access?

    1. (1, 0)
    2. (0, 1)
    3. (-1, -1)
    4. $\left(\frac{1}{2}, 0\right)$

  2. Which point is on the x-access?

    1. (1, 0)
    2. (0, 1)
    3. (-1, -1)
    4. $\left(\frac{1}{2}, 0\right)$

  3. Which point is an y-intercept?

    1. (1, 0)
    2. (0, 1)
    3. (-1, -1)
    4. $\left(\frac{1}{2}, 0\right)$

  4. Which point is a x-intercept?

    1. (1, 0)
    2. (0, 1)
    3. (-1, -1)
    4. $\left(\frac{1}{2}, 0\right)$

  5. What is a good visual test for a linear function?

    1. A vertical line
    2. An infinite line

  6. Which of the following CAN NEVER be a linear function?

    1. A horizontal line
    2. A straight line
    3. A vertical line
    4. An infinite line

  7. Which set of ordered pairs satisfies a linear function?

    1. { (5 ,1), (4 , 4), (3, 9), (2 , 16), (1 25) }
    2. { (1, -5), (2 , -3), (3, -1), (4 , 1), (5, 3) }

  8. Which set of ordered pairs is an arithmetic sequence?

    1. { (5 ,1), (4 , 4), (3, 9), (2 , 16), (1 25) }
    2. { (1, -5), (2 , -3), (3, -1), (4 , 1), (5, 3) }

  9. Convert to Standard Form: $y=2x+1$

  10. What is the Standard Form of a linear function?

  11. What is the Slope-Intercept Form of a linear function?

  12. Which is NOT true about the Standard Form?

    1. The variable are written in alphabetical order.
    2. The x variable must always be positive.
    3. Fractions are NOT allowed.
    4. The y variable must always be positive.

  13. What is the Slope Formula?

  14. Why is it so easy to plot lines using x- and y-intercepts?

  15. Which is true about a positive slope?

    1. The line goes up and to the right.
    2. The line is horizontal.
    3. The line goes down and to the right.
    4. The line is vertical.

  16. Which is true about a negative slope?

    1. The line goes up and to the right.
    2. The line is horizontal.
    3. The line goes down and to the right.
    4. The line is vertical.

  17. Which is true about a zero slope?

    1. The line goes up and to the right.
    2. The line is horizontal.
    3. The line goes down and to the right.
    4. The line is vertical.

  18. Which is true about an undefined (or infinite) slope?

    1. The line goes up and to the right.
    2. The line is horizontal.
    3. The line goes down and to the right.
    4. The line is vertical.

  19. Find the slope of a line with points (-2, -1) and (4, 2).

  20. Find the slope of a line with points (0, 2) and (4, -1).

  21. Write equations in Standard Form representing each of the following:

    1. A positive slope.
    2. A negative slope.
    3. A horizontal line.
    4. A vertical line.

Video: Linear Equations in the Real World (13:08)

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