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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.

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Unit B: Linear Equations

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  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).

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