1 / 27

Graphing lines using the equation

Graphing lines using the equation. Identify the Y-intercept (b) and graph it on the y-axis with a point. Identify what the slope is (m) . Remember slope is rise over run.

cecily
Download Presentation

Graphing lines using the equation

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. Graphing lines using the equation • Identify the Y-intercept (b) and graph it on the y-axis with a point. • Identify what the slope is (m). Remember slope is rise over run. • From the point on the y-axis, if your slope is positive go up or if it is negative go down whatever the RISE is. Go over to the right for the run. Mark the spot with a point. • Draw a line thru those two points

  2. Y= 2/3 x + 3 • Go to the y-axis and draw a point at 3. • From that point go up 2 units and over 3 units. Draw a point. • Draw a line thru those two points. • That is how easy it is to graph lines.

  3. Y = -3x -1 • Go to the y-axis and draw a point at –1. • From that point go down 3 units and over 1. Draw a point. • Draw a line thru those points. • Wow that was easy!

  4. Y= 2 • Draw out a two column box. The first column is labeled X and the second column is labeled Y. • Fill the Y column with values of 2 because the equation said so. • Pick any values for x. • Now graph those ordered pairs and draw a line thru those points.

  5. X= -4 • Make a chart again like last time. • But, All the values for x are –4’s. Because our equation said so. • You decide the values for the y’s. • Now graph the ordered pairs and draw a line thru those points.

  6. Practice converting linear equations into Slope-Intercept Form It’s easier than you think…

  7. Slope intercept form is: y = mx + b Our main goal is to get the y alone on one side of the equation

  8. Convert Into Slope-Intercept Form (divide both sides by 2 to get y alone) (now simplify all fractions) 2 1

  9. Intercept slope Now look at the equation below…… When an equation is in slope-intercept form: y = mx + b 2 What is the slope? ____________ 1 What is the intercept? ____________

  10. Now look at the graph of the line. y = 2x + 1 Step 1: Look at the y-intercept and plot where the graphs cross the “y” axis. Step 2: Use the slope (rise/run) to determine the next point and plot. Step 3: Draw a line through both points. Be sure to extend pass point and put arrow at both ends.

  11. *** Easy *** Convert to Slope-Intercept Form: 5y = 10x + 15 (divide both sides by 5 to get y alone) (now simplify all fractions) y = 2x + 3 BRAVO!!

  12. *** Now Try this Convert to Slope-Intercept Form*** -3y = -9x - 12 Step 1: divide both sides by -3 to get y alone Step 2: Simplify all fractions Step 3: Write your equation in y = mx + b What is the slope? ____________ What is the intercept? ____________

  13. -3-3 -3y = -9x - 12 -3-3 -3 *** Check Your Answer *** -3y = -9x - 12 (divide both sides by -3 to get y alone) (now simplify all fractions) y = 3x + 4 Wow, you’re good at this!! Slope = 3 Intercept = 4

  14. *** medium *** Convert to Slope-Intercept Form: 21x – 7y =14 (subtract both sides by 21x) (now divide both sides by -7) -7y = -21x + 14 (simplify all fractions) y = 3x – 2

  15. *** Now Try this Convert to Slope-Intercept Form*** 2y + 26 = -6x Step 1: Subtract both sides by 26 Step 2: Divide both sides by 2 to get y by itself Step 3: Simplify all fractions What is the slope? ____________ What is the intercept? ____________

  16. *** Check Your Answer*** 2y + 26 = -6x (subtract both sides by 26) (now divide both sides by 2 2y = -6x - 26 (simplify all fractions) y = -3x - 13 You are a math wizard!

  17. Graphing Linear Equations In Slope-Intercept Form

  18. We have already seen that linear equations have two variables and when we plot all the (x,y) pairs that make the equation true we get a line. In this section, instead of making a table, evaluating y for each x, plotting the points and making a line, we will use The Slope-Intercept Form of the equation to graph the line.

  19. These equations are all in Slope-Intercept Form: Notice that these equations are all solved for y.

  20. Just by looking at an equation in this form, we can draw the line (no tables). • The constant is the y-intercept. • The coefficient is the slope. Constant = 1, y-intercept = 1. Coefficient = 2, slope = 2. Constant = -4, y-intercept = -4. Coefficient = -1, slope = -1. Constant = -2, y-intercept = -2. Coefficient = 3/2, slope = 3/2.

  21. The formula for Slope-Intercept Form is: • ‘b’ is the y-intercept. • ‘m’ is the slope. On the next three slides we will graph the three equations: using their y-intercepts and slopes.

  22. right 1 up 2 right 1 up 2 1) Plot the y-intercept as a point on the y-axis. The constant, b = 1, so the y-intercept = 1. 2) Plot more points by counting the slope up the numerator (down if negative) and right the denominator. The coefficient, m = 2, so the slope = 2/1.

  23. down 1 down 1 right 1 right 1 1) Plot the y-intercept as a point on the y-axis. The constant, b = -4, so the y-intercept = -4. 2) Plot more points by counting the slope up the numerator (down if negative) and right the denominator. The coefficient, m = -1, so the slope = -1/1.

  24. right 2 up 3 right 2 up 3 1) Plot the y-intercept as a point on the y-axis. The constant, b = -2, so the y-intercept = -2. 2) Plot more points by counting the slope up the numerator (down if negative) and right the denominator. The coefficient, m = 3/2, so the slope = 3/2.

  25. Sometimes we must solve the equation for y before we can graph it. The constant, b = 3 is the y-intercept. The coefficient, m = -2 is the slope.

  26. down 2 down 2 right 1 right 1 1) Plot the y-intercept as a point on the y-axis. The constant, b = 3, so the y-intercept = 3. 2) Plot more points by counting the slope up the numerator (down if negative) and right the denominator. The coefficient, m = -2, so the slope = -2/1.

More Related