Warm up 1.Find the slope of a line that passes through these points: a.B(2,5) C(3,1)b. L (4,3) M (-2, -6) 2.Write each equation in its simplest form: a.

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Warm up 1.Find the slope of a line that passes through these points: a.B(2,5) C(3,1)b. L (4,3) M (-2, -6) 2.Write each equation in its simplest form: a. -3 (x+6) b. -1/4(4x-8) +18

I can write a linear equation in different forms.

Types of Equations y- intercept or slope-intercept form y= mx + b Standard form Ax + By = C Point slope form y - y 1 = m(x - x 1 )

Slope-Intercept Form y=mx+b m is the slope and b is the y-intercept

Standard Form Ax + By = C A and B are not both zero. Usually A is non-negative and A, B, and C are integers whose greatest common factor is 1.

Point-Slope Form

Point Slope Form y - y 1 = m(x - x 1 ) Example: (-1, 5) m= -3 y- 5 = -3[x -(-1)] y - 5= -3(x + 1) Remember: (x 1, y 1 ) represents the given point and (x,y) represents any other point on the line.

Write the equation from Point-Slope form to Slope-intercept form y -5 = -3 (x + 1) y-5 = -3x - 3 Distribute Add 5 to both sides y= -3x + 2 Simplify

Write the equation in Standard Form y = -3x x +3x add 3x to both sides 3x + y = 2 Rules: In standard form the equation is in Ax + By = C form. A, B, and C have to be integers and A can’t be negative. (no fractions or decimals)

Write the point-slope form of an equation for a line that passes through (3,8) and has a slope of 2 y - y 1 = m(x - x 1 ) Why learn this equation when we have y-intercept form? You will need it to help you solve problems related to transformations on a coordinate plane.

Practice Write an equation in Point-Slope Form, Standard Form and Slope-Intercept Form for each line. 1.Passes through (1,9), slope =2 2.Passes through (4,1), slope =-3 3.Passes through (4, -4) and (8, -10) 4.Passes through (3,4) and (5, -4)

Here’s your cheat sheet! If the equation is in STANDARD FORM (Ax + By = C), graph using the intercepts. If the equation is in SLOPE-INTERCEPT FORM (y = mx + b), graph using slope and intercept (whichever is easier for you). If the equation is in neither form, rewrite the equation in the form you like the best!

Graph -2x + 3y = 12 Which graphing method is easiest? Using x- and y-intercepts! (The equation is in standard form) Remember, plug in 0 to find the intercepts.

1.Find your x-intercept: Let y = 0 -2x + 3(0) = 12 x = -6; (-6, 0) 2.Find your y-intercept: Let x = 0 -2(0) + 3y = 12 y = 4; (0, 4) 3.Graph both points and draw a line through them. Review: Graphing with intercepts: -2x + 3y = 12

Which method is easiest to graph -3x + 6y = 2? 1.T-table 2.Slope and intercept 3.X- and Y-intercepts 4.Graphing calculator

Which is the graph of y = x + 2?