Point Slope Form To write an equation with the slope and a point that is not the y intercept

Point Slope Form y – y₁ = m(x – x₁) You only need ONE point and the slope!!!! Example: m = 4 (-2, 3) y – 3= 4(x - -2) y – 3= 4(x + 2)

Standard Form Standard Form of a linear Equation Ax + By = C A and B do not equal zero A, B, and C are not fractions! How do we write an equation in standard form? We make sure that the variables x and y are both on the same side of the equal sign. We can use pt. slope form to help us with standard form

y – 3= 4(x + 2) y – 3 = 4x x -4x + y – 3 = x + y = 11 or 4x – y = -11 Example: (3,5) m = - ¼ y – 5 = -¼(x – 3) Y – 5 = -¼x + ¾ *Clear fractions* Multiply by the LCD 4( Y – 5 = -¼x + ¾) 4y – 20 = -1x x X + 4y – 20 = X + 4y = 23

Practice: Write the equation of the line that passes through (2, -4) with a slope of -3 in Standard Form Practice: Write the equation of the line that passes through (5, -6) with a slope of ½ in Standard Form Answers: 3x + y = 2 or -3x – y = -2 X – 2y = 17 or –x + 2y = -17

What happens when we do not have a slope? Write the equation of the line that goes through the points: (1,3) and (5, -2) Find the slope first! = 5 = m 1 – 5 -4 Now you can use either pt for pt. slope form. y – 3 = -5 (x – 1) 4 y + 2 = -5 (x – 5) 4 Answer: 5x + 4y = 17

Review: Vertical lines are “x” = # Horizontal lines are “y” = # What if I want to write an equation that is vertical going through the point (4, 3)? Think about which coordinate we need! Our equation for a vertical line would be: X = 4 What about Horizontal? Y = 3