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**Warm up Graph the equation of the line using slope & y-intercept**

4x – 2y = 10

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**Lesson 8-5 Determining an Equation of a Line**

Objective: To find an equation of a line given the slope and one point on the line, or given two points on the line.

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**Finding the Equation of a Line**

If you know that the slope-intercept form of a line is y = mx + b then you can find the equation of any line if you know any 2 of the following: a) slope b) y-intercept c) a point on the line d) x-intercept ( some point in which the y is 0) ( where the line crosses the x axis)

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y = mx + b Example: if the slope is 4 and the y-intercept is -6 then the equation is y = 4x-6

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Example 2 Write the equation of a line that has a slope of - 3 and an x-intercept of 1/3. Solution: You can plug in the slope immediately so y = -3x + b The x-intercept is just a point on the line where y is 0, so the point is (1/3,0) Any time you have a point you can plug it into the partial equation and then solve for the missing term. 0 = -3(1/3) + b

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**Now just solve for b so 0 = -1 +b**

Once you have b you can write the equation y = -3x + 1

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Example 3 Write the equation of the line passing through the points (1,1) and (2,4) Solution: If you have 2 point you can find the slope so 4-1 = 3 = 3 then you can use one of the points the same way we used the x-intercept in example 2 y = 3x + b (using (1,1) 1 = 3(1) + b 1 = 3 + b -2 = b y = 3x -2 is the equation of the line

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**Practice Find the equation of the line when**

1. slope is 2 and y-intercept is 15 2. slope is -3 and x-intercept -3 3. Line passes through the points (4, - 3), ( 3, -6)

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