Writing Equations of Lines. What am I learning today? How can you find an equation of a line given the slope and the y intercept of the line? Given the.

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Writing Equations of Lines

What am I learning today? How can you find an equation of a line given the slope and the y intercept of the line? Given the slope and a point on the line? Given two points on the line?

I. How to Write an Equation of a Line Given m and b 1. Write down y = m x + b 2. Substitute slope for m and y-intercept for b. 3. Simplify the equation

Write the equation of the line given m and b. Ex. 1 Slope is -5 and y-intercept is 2 Ex. 2 Slope is -1/2 and y-intercept is -2 y = -5x + 2 y = -½x – 2

Write the equation of the line given m and b. Ex. 3 Slope is 0 and y-intercept is 3 Ex. 4 Slope is 1/3 and y-intercept is 0 y = 3

II. How to Write an Equation of a Line Given a Graph 1.Write down y = mx + b 2.Use any 2 “good” points on the graph to find the slope, m. 3.Find the y-intercept on the graph, b. 4.Substitute slope for m and y-int for b into the equation y = m x + b.

5. Write the equation of this graph  

6. Write the equation of this graph  

7. Write the equation of this graph   y = -3x + 2

8. Write the equation of this graph y = 2x  

9. Write the equation of this graph y = 3 

10. Write the equation of this graph x = - 6

11. & 12. Write the equation of each graph y = 2x – 3y = -3/2x + 3    

III. How to Write an Equation of a Line Given m and a point 1.Write down y = mx + b. 2.Substitute slope for m and the point (x, y). 3.Solve for b. 4.Substitute m and b back into the equation.

Write the equation of the line given m and a point Ex 13: m = 2Point: (2, 3) y = mx + b 3 = 2 (2) + b b = -1 y = 2x – 1

Ex 14: m = 1/2Point: (4,-3) y = mx + b -3 = 1/2 (4) + b b = -5 y = ½ x – 5 Write the equation of the line given m and a point

Ex 15: m = -2Point: (-5, 3) y = mx + b 3 = -2 (-5) + b b = -7 y = -2x – 7 Write the equation of the line given m and a point

Ex: 16 m = 4 (1,4) y = 4x Write the equation of the line given m and a point

Ex: 17 m = ½ (-1,-2) y = ½ x – 1 ½ Write the equation of the line given m and a point

Ex: 18 m = 2 (0,3) y = 2x + 3 Write the equation of the line given m and a point

Ex: 19 m = 3 (3,0) y = 3x – 9 Write the equation of the line given m and a point

Ex: 20 m = undefined (3,6) x = 3 Write the equation of the line given m and a point

IV. How to Write an Equation of a Line Given TWO points 1.Write down y = mx + b. 2.Use the slope formula to find m. 3.Pick one of the ordered pairs & substitute slope for m and the point (x, y). 4.Solve for b. 5.Substitute m and b into the equation.

Equation of a Line - Given 2 points Ex: 21 (2, 3) (4, 5) y = mx + b 3 = 1(2) + b b = 1 y = x + 1

Equation of a Line - Given 2 points Ex: 22 (2, 3) (-4, 15) y = -2x + 7

Equation of a Line - Given 2 points Ex: 23 (2, 2) (0, 4) y = -x + 4

Equation of a Line - Given 2 points Ex: 24 (2,3) (1,4) y = -x + 5

Equation of a Line - Given 2 points Ex: 25 (4,5) (5,2) y = -3x + 17

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