Writing an Equation of a Line I can…. determine the equation of a line and/or graph a linear equation. 1-24-13 Unit 1 Basics of Geometry.

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Writing an Equation of a Line

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Writing an Equation of a Line I can…. determine the equation of a line and/or graph a linear equation Unit 1 Basics of Geometry

Forms of a linear equation Slope-intercept Formy = mx + b Standard FormAx + By = C Point-Slope Formy – y 1 = m(x – x 1 )

The method used to write an equation of a line depends on the information about the line that is available.

If given the slope and y-intercept, use slope-intercept form. 5 Example m = 5, b = 7 y = ___ x + ___ 7

If given the a point and the slope, There are two methods that are both effective. The time required and the number of steps for the two methods is comparable. Know how to do both, but typically either will work just fine.

If given the a point and the slope, Method 1 use slope-intercept form. Example m = –2, contains (5, –8) Step 1 Substitute –2 for m, 5 for x, and –8 for y; then simplify to find the value of b. y = mx + b –8 = –2(5) + b –8 = –10 + b 2 = b Step 2 Substitute –2 for m, and 2 for b. y = –2x + 2

If given the a point and the slope, Method 2 use point-slope form. Example m = –2, contains (5, –8) Substitute –2 for m, 5 for x 1, and –8 for y 1 ; then simplify and solve the equation for y. y – y 1 = m(x – x 1 ) y – (– 8) = – 2(x – 5) y + 8 = –2x + 10 y = –2x + 2

If given two points, First, find the slope using the slope formula. Example contains (5, –8) and (2, 7) m = 7 – – 5 m = 15 –3 m = –5

If given two points, Then use the slope and EITHER point to work like the previous example. y – y 1 = m(x – x 1 ) y – 7 = – 5(x – 2) y – 7 = –5x + 10 y = –5x + 17 m = –5, contains (5, –8) and (2, 7)