Standard Form What you’ll learn To graph linear equations using intercepts To write linear equations in standard form x-intercept, standard form of a linear equation

Just a note a very important NOTE Remember: What is the y-intercept? and x=0Where the line crosses the y-axis Now the x-intercept is the x coordinate of a point where the graph crosses the x-axis and y=0 From the graph on the left name the x-intercept and the y-intercept for each line 1 2 Line 1 (0,3) (-4,0) y-intercept x-intercept Line 2 (0,-4) (-2,0)

Standard Form of a Linear Equation hThe standard form of a linear equation is where A,B,and C are real numbers and A and B are not both zero. Examples: 4x+2y=13 5x-2y=-6 Ax+By=C

Finding the x and y intercept What are the x and the y intercepts of the graph 3x+4y=24 Step 1: to find the x-intercept, make y=0 (8,0) Step 2: to find the Y-intercept, make x=0 (0,6)

Your turn What are the x and y intercept of the graph of each equation? a) 5x-6y=60 b) 3x+8y=12 Answers: a) (0,-10) and (12,0) b) (0,1.5) and (4,0) Graph them a) b)

Notes If A=0 in the standard form Ax+By=C then you can write the equation in the form y=b, where b is a constant and the graph will be a horizontal line If B=0 in the standard form Ax+By=C then you can write the equation in the form x=a, where a is a constant and the graph is a vertical line

Your turn What is the graph of each equation? Write them in the standard form A. x=3 B. y=3 C. x=4 D. x=-5 E. y=0 E C A D B Answer

Using the Standard Form as a Model A media download store sells songs for $1 each and movies for $12 each. You have $60 to spend. Write and graph an equation that describes the items you purchase. What are three combinations of numbers of songs and movies you can purchase? Let x= the number of songs Let y= the number of movies 1x+12y=60 X=0 so 12y=60 y=5 Y=0 so x=60 (0,5) (60,0) (24,3)

Your turn a) Can you buy half of a song or a movie? No, the graph is a line but only points with integers coordinates are solutions. b) Suppose the store charged $15 for each movie. What equation describes the numbers of songs and movies you can purchase for $60? c) What domain and range are reasonable for the equation in part b). Explain X+15y=60 Domain: non negative integers less than or equal to 60 Range: {0,1,2,3,4}

Notes Given the graph Slope intercept form y=mx+b Point Slope Form Standard Form Ax+By=C 2x+3y=18 y-intercept (0,6 ) x-intercept (9,0) Point(3,4) Slope m=-