Point Slope Form

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

• Point Slope Formy – 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 + 8-4x -4x-4x + y – 3 = 8 + 3 + 3

-4x + y = 11 or4x – y = -11

• Example: (3,5) m = -¼

y – 5 = -¼(x – 3)Y – 5 = -¼x + ¾*Clear fractions*Multiply by the LCD4(Y – 5 = -¼x + ¾)4y – 20 = -1x + 3+1x +1xX + 4y – 20 = 3

+ 20 + 20X + 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 ½in 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!

3 - -2 = 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