1 / 23

Unit B: Linear Equations

Unit B: Linear Equations. B.1 Introduction to Linear Equations and Slope. What is a linear equation?. An equation that has no operation other than addition, subtraction, and multiplication of a variable by a constant. The variables may not be multiplied together, or appear in a denominator.

gabe
Download Presentation

Unit B: Linear Equations

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Unit B: Linear Equations B.1 Introduction to Linear Equations and Slope

  2. What is a linear equation? • An equation that has no operation other than addition, subtraction, and multiplication of a variable by a constant. • The variables may not be multiplied together, or appear in a denominator. • Do not contain variables with an exponent other than 1.

  3. Examples and non-examples Examples Non-Examples 7a+4b2 = -8 X+xy=1 Y=1/x • 5x-3y=7 • X=9 • 6s=-3t-15 • Y=1/2 x

  4. Example 1 • State whether each is a linear equation. Explain. • Y=10-5x • Y=x4-5 • H=2xy

  5. What is a linear equation? • The SOLUTIONS to a linear equation are the values of (x,y) that make the equation balance. • To find solutions to any equation, plug in whatever you want to x, then solve for y. • How many solutions can you find to the equation y=2x?

  6. The solutions can be represented by using the order pairs, or you can draw them on a graph. • Let’s draw the solutions to y=2x on the graph.

  7. Intercepts • Intercepts are the points on a graph where the line passes through the x- and y-axis. • What would the x- and y-intercepts of this graph be?

  8. Slope • The slope of a line is the ratio of the change in the y-coordinates to the change in the x-coordinates. • Basically, it represents how steep the line is. • There are two ways we can find slope.

  9. Rise over Run • When given a graph, it is pretty easy to find the slope of the line. • 1. Find two points where the x and y are whole numbers. • 2. Count how many up or down you have to go, then count how many left or right you have to go to get from one point to another.

  10. Example 2 • Find the slope of this line. • Remember: Rise OVER run

  11. Example 3 • Find the slope of this line. • Remember: Rise OVER run

  12. Pos/neg zero undefined

  13. Finding Slope Using Ordered Pairs • Use the formula: • m= y-y/x-x • Where the first y and x must come from the same ordered pair.

  14. Example 4 • Find the slope of the line that passes through the points (-3,2) and (1, -4). • Find the slope of the line that passes through the points (-4,-3) and (2,1).

  15. Equations of Lines • The equation of a line in slope-intercept form is • Y=mx+b where m is the slope and b is the y-intercept. • Example: What is the slope and the y-intercept of Y=2x+4?

  16. Example 5 • Write the equation of a line that has a slope of 3 and a y-intercept of -1.

  17. Example 6 • What is the slope and y intercept of the line 2x+4 = 2y? • What is the slope and y-intercept of the line 12x-4y=8x?

  18. Example 7 • Write the equation of the line that goes through (3,1) and (2,2). • Write the equation of the line that goes through (-1,-1) and (4,5).

  19. Graphing Lines Given the Equation • To graph a line, put it in slope-intercept form (solve for y). • Then, graph the y-intercept. • Lastly, use the slope to graph another point.

  20. Example 8 • Graph the line x-y=6.

  21. Example 9 • Write the equation of the line shown below.

  22. Equations of Vertical and Horizontal Lines • Horizontal: Remember HOY • H=horizontal • 0=zero slope= • Y=# is the equation • Vertical: Remember VUX • V=vertical • U=undefined slope • X=# is equation

  23. Example 10 • Graph the line that has an undefined slope and passes through (1,2). • Graph the horizontal line that passes through (0,1).

More Related