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2.4 Writing Equations of Lines

Learn three methods to write equations of lines given specific information such as slope, y-intercept, or points on the line. Includes examples and step-by-step instructions.

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2.4 Writing Equations of Lines

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  1. 2.4 Writing Equations of Lines

  2. We’ve learned to graph given an equation. • Now we’ll learn to write the equation given the graph • There are three ways. • It all depends on what information you are given as to which process you use.

  3. Given the slope, m, and the y-intercept, b, use the equationy=mx+b • The y-intercept is -3 • b=-3 • The slope is 4/3 • The equation is: • y = 4/3x – 3 3 4

  4. Use Point Slope Form:If you are given slope, m, and a point (x1,y1) on the line • y – y1 = m ( x – x1)

  5. Write an equation of a line containing the point (1,2) with slope of -1/2. • Use (x1,y1) = (1,2) & m = -1/2 • y – 2 = -1/2 ( x – 1) • Now you can simplify to the slope intercept form • y – 2 = -1/2 x + ½ • y = -1/2 x + 5/2

  6. If you are given two points on the line • Find the slope using the two points • Then plug this slope and either one of the points into the point slope formula.

  7. Given two points (-2,2) & (3,7) • Find the slope: • m=1 • Plug this slope and one of the points into the point slope formula. • y – 2 = 1 ( x – (-2)) • y – 2 = x + 2 • y = x + 4 (put the equation into slope intercept form) (3,7) (-2,2)

  8. Direct Variation • 2 variables X & Y show direct variation provided y = kx & k ≠ 0. • The non-zero constant k is called the constant of variation, & y is said to vary directly with x. • The graph of y=kx is a line thru the origin.

  9. The variables x & y vary directly, & y = 12 when x = 4. Write and graph an equation relating x & y. • Use x & y to find the constant of variation • y = kx • 12 = k4 • 3 = k • The direct variation equation is y = 3x • This is what you MUST write as the answer!

  10. Graph y = 3x

  11. In the same direct variation equation, when x=5, find the value of y. • y = 3*5 • y = 15

  12. Assignment

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