To write equations of lines in the point-slope form.

Essential question  What are the different ways to write the equation of a line. 

Do Now – Match the equations on the left with an equations on the right Point-Slope  Slope-intercept  y – 8 = ½ (x + 6) y + 2 = 3(x – 4)  y – 9 = x + 4  y = 3x – 14 y  = x + 13   y = ½ x – 2  y = ½x + 11 y = 3x – 5    

Point – Slope Form  The equation of  a slope is 

Point – Slope  https://youtu.be/K_OI9LA54AA 

Example 1: Write an Equation Write an equation in point-slope form for the line that passes through (3, -2) with a slope of ¼. Then graph the equation. y - (-2) = ¼ (x – 3) y + 2 = ¼ (x – 3) To graph plot (3, -2) and use the slope to move.

Writing Equations in Point-Slope Given the Slope and the Point  Given Two Points  Substitute m, and the coordinates are (x1, y1).  Rewrite the equation in the needed form.  Find the slope. Choose one of the two points to use.  Follow the steps for writing the equation with the slope and one point. 

Another Example  https://youtu.be/0bqr9Fo3Qi8 

Example 2: Standard Form Write y – 1 = - 2/3(x – 5) in standard form. Hint: What is standard form?

Solution y – 1 = -2/3 (x – 5) 3(y –1) = 3(-2/3)(x – 5) Multiply both sides by 3.  3(y – 1) = -2(x – 5)  3y – 3 = -2x + 10  Distribute to eliminate ( ) 3y – 3 + 3 = -2x + 10 + 3 Add 3 to both side   3y = -2x + 13  3y + 2x = -2x + 2x + 13 Add 2x to both side  2x + 3y = 13

Example 3: Slope – Intercept Form Write y + 3 = 3/2 (x + 1) in slope – intercept form. y + 3 = 3/2 (x + 1) y + 3 = 3/2x + 3/2 distribute 3/2 y+ 3 - 3 = 3/2x + 3/2 - 3 subtract 3 from both sides y = 3/2x + 3/2 - 6/2 change 3 to 6/2, we need the same denominator y = 3/2x - 3/2

Activity – Match each graph to the appropriate equation. 1 y + 7 = 3(x + 2)  y – 7 = 3(x – 2) 

Activity  y + 2 = ½ (x – 2)  y – 2 = ½ (x + 2) y – 2 = 2 (x + 2)    

Classwork/ Homework  Classwork: 4 – 3 Skills Practice (Odd) Homework: 4 – 3 Skills Practice (Even)