3-3 Linear Equations A linear equation is an equation of a line. A linear equation is an equation that can be written in STANDARD FORM Where A, B, and C are any numbers A & B are not both zero A can not be a fraction or negative

Is it a linear equation? xy = 2 x2 = y2 3m – 2n = 8 3m – 2n = 0 No x2 = y2 3m – 2n = 8 Yes 3m – 2n = 0 4x2 – 3x = y 2m + 5m = 7n

Determine whether the equations are linear equations Determine whether the equations are linear equations. If so, write the equation in standard form. 5x + 3y = z + 2 Not linear one too many variables .75x = y + 8 Linear change to standard form Ax + By = C .75x – y = 8 subtract y from both sides 3/4x – y = 8 change .75 to a fraction of 3/4 4(3/4x – y) = 4(8) multiply each side by denominator of 4 3x – 4y = 32 distribute 1/3y = -1 Linear y = -3 y = x2 + 3 Not linear x is squared

X & Y Intercepts X – intercept (aka zeros): The x-coordinate of the point at which the graph of an equation crosses the x-axis. Where the y value is 0 Y – intercept: The y-coordinate of the point at which the graph of an equation crosses the y-axis. Where the x value is 0 x-intercept y-intercept

Let’s take a look at pg. 156 Check your Progress 2A & 2B Determine the x-intercept, y-intercept, and zero. None, 150, none Remember – the x-intercept and the zero will always be the same! Describe what the intercepts mean. The y-intercept 150 means that the initial cost of the gym membership is $150.

Now take a look at pg. 157 Check your Progress #3 Use the table (in example #3) to determine the x-intercept, y-intercept, and zero of the graph of the function. x = -2 y = -4 Zero: x = -2

Graphing by making a table x 2x + 2 y (x,y) -2 2(-2) + 2 (-2,-2) -1 2(-1) + 2 (-1,0) 2(0) + 2 2 (0,2) 1 2(1) + 2 4 (1,4) 2(2) + 2 6 (2,6) Graph ½y – x = 1 Get y by itself ½y = x + 1 y = 2x + 2 Pick values for x and plug them in to get y. Pick 2 negative, 0, and 2 positive numbers.

Now Graph it (x,y) (-2,-2) (-1,0) (0,2) (1,4) (2,6)

3x + 4y = 12 Let x = 0 OR simply cover up 3x. What does y equal? 3 Plot it on the y-axis. Let y = 0 OR simply cover up 4y. What does x equal? 4 Plot it on the x-axis Then use a straightedge and connect the dots.

X = 2 Y = 3 Y = 3 means y is 3 regardless of what x is. Y = # is always a HORIZONTAL LINE! X = 2 means x is 2 regardless of what y is. X = # is always a VERTICAL LINE!

Try These – Pg. 158 #1-4, 7-8, 10 1. No 2. Yes; 3y = -2 3. Yes; 3x – 2y = 25 4. 25, -4; x – intercept: temp at 0. y – intercept: at time 0, temp is -4 7. y = 2x + 8 8. x = 3 10. x + 4y = 10

Homework #22 p.159 13-51(odd), 61-63, skip 37