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Slope-Intercept Form

Slope-Intercept Form

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Slope-Intercept Form

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  1. Slope-Intercept Form Linear Equations

  2. What is Slope-Intercept Form? • Slope-Intercept form is a way a line can be written. • It includes the slope and the y-intercept. • The equation is y=mx + b, where m = the slope and b = the y-intercept

  3. An Example of Slope-Intercept • When given y=2/3x – 2, graph the linear equation. • First, what is the y-intercept? • The y-intercept is -2! • Then, find the slope…… • The slope is 2/3. What does that mean? • From each point, the line will rise up 2 and go right 3.

  4. How do I Graph with Slope-Intercept? The equation was y=2/3x – 2. 1st – Find the y-intercept…. -2, and place it on the graph 2nd – Find the slope….. The slope is 2/3. Rise/Run so the graph rises up 2 and runs 3. 3rd– Plot another point by following the slope. The next point will be at (3, 0). 4th – Connect the two with a line.

  5. How Do I Write an Equation in Slope-Intercept Form When Given a Graph? You need two things: SLOPE AND Y-INTERCEPT 1st – Find the y-intercept. Where does the line cross the y-axis? The y-intercept is 4! 2nd – Is it a positive or negative slope? Does it go up or down from left to right? It goes down so it’s NEGATIVE! 3rd – Find another point where the line crosses a grid intersection. There is one at (1, 1)! 4th – Count the rise/run from the y- intercept to the second point. The line went down 3 and right 1. So the slope is -3/1 which is -3. So, if slope is -3 and the y-intercept is 4, what is the equation?...... y = -3x + 4

  6. Standard Form Linear Equations

  7. What is Standard Form? • Standard form is another way to write a linear equation. • The equation is …. ax + by = c • A and B are coefficients for the variables. • C is a number.

  8. How Can I Graph from Standard Form? You only need two points to draw a line. Standard Form gives you the two points…..the x and y intercepts! 3x - 6y = 12 1st – Find the x-intercept. Make y = 0 3x - 6(0) = 12 3x - 0 = 12 3x = 12 so…… x intercept is 4!!! 2nd – Find the y-intercept. Make x = 0 3(0) - 6y = 12 0 - 6y = 12 -6y = 12 so…… y = -2 Connect the dots by drawing a straight line. You have now graphed your line.

  9. How Can I Write Slope-Intercept Equations in Standard Form? • When given y = 3x – 2, write the equation in standard form • Remember, Standard Form is ax + by = c. • Follow these easy steps: • y = 3x – 2 -3x -3x (subtract 3x from each side) -3x + y = -2 or if you change the signs…… 3x – y = 2…..either answer is acceptable.

  10. Let’s Try Some More Write the following in Standard Form: • y = 6x + 7 • y = 3x – 4 • y = -3x + 1 • y = 4x • Answers: • y = 6x + 7  -6x + y = 7 or 6x – y = -7 • y = 3x – 4  -3x + y = -4 or 3x – y = 4 • y = -3x + 1  3x + y = 1 • y = 4x  -4x + y = 0 or 4x – y = 0

  11. WHAT ABOUT FRACTIONS??? • y = -¾ x + 4 + ¾x +¾x ( add ¾x to both sides) ¾x + y = 4 (There’s an ugly fraction there…ugh!) How do you get rid of a FRACTION???? Multiply by the denominator.... Multiply EVERYTHING!! (4) (¾x) + (4)y = (4)4 The four cancelled out the fraction….YEAH!!! 3x + 4y = 16

  12. Let’s Try Some More • y = ½x – 2 • y = 1/3x + 4 • y = ¼x – 2 • y = 2/5x + 1 • Answers: • y = ½x – 2  -x + 2y = -4 or x – 2y = 4 • y = 1/3x + 4  -x +3y = 12 or x – 3y = -12 • y = -¼x – 2  x + 4y = -8 • y = -2/5x + 1  2x + 5y = 5

  13. How Do I Write Standard Form in Slope-Intercept Form? • SOLVE FOR Y!! • When given 2x + 3y = 9, write in slope-intercept form • How do I solve for y??? • First get y by itself…..subtract 2x from both sides • 2x + 3y = 9 -2x -2x 3y = -2x + 9 (You have to write the x first) 3 3 3 (Then divide by 3…EVERYTHING) • So y = -2/3x + 3

  14. Let’s Try Some More • Write in Slope-Intercept Form • 2x + 4y = 12 • -3x + 5y = 10 • x – 2y = -6 • 6x – 4y = 3 Answers: • y = -½x +3 • y = 3/5x + 2 • y = ½x + 3 • y = 3/2x – ¾

  15. Point-slope Form Linear Equations

  16. What is Point-Slope Form • It is another way to write a linear equation. • You need a point and the slope (hint: the name) • The formula is y – y1=m(x – x1) • m= the slope • (x1, y1) is the point.

  17. How do I write an equation in point slope form? • What is the equation for the line that runs through (3, 4) and has a slope of -½ • m= -½ • (3 is x1, 4 is y1) • Put it into the equation!!! • y- 4 = -½(x – 3) • And that’s it…..Nothing More!!! What do you think will be the most common mistake people will make?..... Putting the x and y’s in the wrong places!!!

  18. How can I graph from Point-Slope form? Graph y – 1 = 1/3 (x – 2) 1st- What is the point? (2, 1) 2nd – Place the point onto the graph 3rd- What is the slope? m = 1/3 4th – From the point (2, 1) rise up 1 and go right 3. 5th – Finally, draw a line to connect the points.