This document summarizes how to write linear equations in standard form and point-slope form. It explains how to write an equation in standard form by moving the x term to the same side as the y term. It then explains how to use the point-slope form, which is y-y1=m(x-x1), to write an equation when given a point and the slope. It walks through examples of using point-slope form to write equations for lines with slopes of 3 and 1/2 when given a point.

1. Standard Form and Point Slope Form

2. Standard Form This linear equation is in standard form. 2x – 3y = 7 This linear equation is in y-intercept form. y= 3 / 2 x + 8

3. Write in Standard Form Start with your equation. Move the x value to the same side as the y value by adding or subtracting the same x values from both sides. +3x +3x

4. Try One Start with your equation. Move the x value to the same side as the y value by adding or subtracting the same x values from both sides. -2x -2x

5. Point Slope Form Find an equation with one set of coordinates and the slope.

6. What’s the Deal? We will now find the y-intercept using Point-Slope form. When complete, our equation will be in y = mx + b form.

7. If y = mx + b, and then y – y 1 =m(x-x 1 ) this is done algebraically by multiplying both sides by (x 2 -x 1 )

8. Related formula

9. y -y 1 = m(x -x 1 )

10. y -y 1 = m(x -x 1 ) We use point slope form (above) when we are given the slope and one point . Such as (-7, 2) with a slope of 3.

11. (-7, 2) with a slope of 3 Start with y -y 1 = m(x -x 1 ) Fill in the slope y -y 1 = 3(x -x 1 ) Fill in the y value y - 2 = 3(x -x 1 ) Fill in the x value y - 2 = 3(x - - 7)

12. Now use what you know about order of operations and balancing like terms. y - 2 = 3(x - - 7) Change the signs (if needed) . y - 2 = 3(x + + 7) Use the distributive property. y - 2 = 3x + 21

13. Add two to both sides. Then solve for y. y – 2 +2 = 3x + 21 +2 y + 0 = 3x + 23 y = 3x + 23

14. (4, 1) with a slope of ½ Start with y -y 1 = m(x -x 1 ) Fill in the slope y -y 1 = ½ (x -x 1 ) Fill in the y value y - 1 = ½ (x -x 1 ) Fill in the x value y - 1 = ½ (x - 4)

15. Distributive Property Then add one to both sides to balance the sides. y - 1 = ½ (x - 4) y - 1 = ½ x – 2 +1 +1 y = ½ x – 1 The slope is ½ and the y-intercept is -1. The equation is ready to graph.

16. y = ½ x – 1

17. Assign: 256 : 29-31 Assign 257: 39 and 40 For numbers 39 and 40 you use yesterday’s information to 1) find the slope, then use the point-slope form ( today’s work ) to find the equation.

18. Copyright D Dahlberg