Chapter 6: Linear Equations & Their Graphs 6.4 Standard Form

Activity: Intercepts Make a table of values for the equation 3y – 2x = 12 xy

Activity: Intercepts Use the table of values to graph 3y – 2x = 12 What is the y- intercept? What is the value of x when the line crosses the x-axis?

Activity: Intercepts In the equation 3y – 2x = 12, what is the value of y when x = 0? What is the value of x when y = 0?

Activity: Intercepts Using your answers from before, how can you graph 3y – 2x = 12 without using a table or doing extensive algebra?

What is an intercept? What is a y-intercept? What is an x-intercept?

Standard Form of a Linear Equation A, B, and C are real numbers, and not zero

Graphing Standard Form You can use intercepts to find two points on the line, and draw it in 1.Plug in zero for “x” and solve for y – This is your y-intercept 2.Plug in zero for “y” and solve for x – This is your x-intercept If you don’t do this, you must use algebra to get it into a different form!

Example 1 Find the x- and y-intercepts of 3x + 4y = 8

Example 1a Find the x- and y-intercepts of 4x – 9y = -12

Example 2 Graph 2x + 3y = 12 using intercepts.

Example 2a Graph 5x + 2y = -10 using intercepts.

Example 3 Graph y = -3

Example 3a Graph x = 2

Example 4 Write y = ¾ x + 2 in standard form using integers.

Example 4a Write y = -2/5 x + 1 in standard form using integers.

Example 5 Write an equation in standard form to find the minutes someone who weighs 150 lb would need to bicycle and swim laps in order to burn 300 calories. Activity by a 150-lb person Calories burned per minute Bicycling10 Bowling4 Hiking7 Running 5.2 mph11 Swimming, laps12 Walking, 3.5 mph5

Example 5a Write an equation in standard form to find the minutes someone who weighs 150 lb would need to bowl and walk to burn 250 calories. Activity by a 150-lb person Calories burned per minute Bicycling10 Bowling4 Hiking7 Running 5.2 mph11 Swimming, laps12 Walking, 3.5 mph5

Homework P even, even, even