6-4: Standard Form Essential Question: How do we convert from y-intercept to standard form?

6-4: Standard Form Slope-Intercept form is just one form of a linear equation. Another form is standard form, which is useful in making quick graphs. Standard Form Ax + By = C, where A, B and C are integers You use the x- and y-intercepts to make a graph. The x-intercept is the x-coordinate where the line crosses the x-axis. You can also find the x-intercept by setting y = 0 and solving

6-4: Standard Form Example 1: Finding x- and y-intercepts Find the x- and y-intercepts of 3x + 4y = 8 x-intercept (set y=0 and solve) 3x + 4(0) = 8 3x = 8 x = 8/3 y-intercept (set x=0 and solve) 3(0) + 4y = 8 4y = 8 y = 2

6-4: Standard Form Your Turn Find the x- and y-intercepts of 4x – 9y = -12 x-intercept x=-3 y-intercept y=4/3

6-4: Standard Form If the x- and y-intercepts are integers, you can use them to make a quick graph Example 2: Graphing Lines Using Intercepts Graph 2x + 3y = 12 Step 1: Find the intercepts Step 2: Plot the intercepts x-intercept 2x + 3(0) = 12 2x = 12 x = 6 y-intercept 2(0) + 3y = 12 3y = 12 y=4

6-4: Standard Form Your Turn Graph 5x + 2y = -10

6-4: Standard Form Example 3: Graphing Horizontal and Vertical Lines y = -3 x = 2 No x-intercept, so the No y-intercept, so the graph doesn’t cross the graph doesn’t cross the x-axis y-axis

6-4: Standard Form You can change equations in slope-intercept form into standard form. If the equations contains fractions or decimals, multiply by the denominator(s) to only use integers Then, add/subtract the x term so that both x and y are on the same side of the equation Example 4: Transforming to Standard Form Write y = ¾ x + 2 in standard form Multiply each term by 4 (the denominator) 4y = 3x + 8 Subtract 3x from each side -3x + 4y = 8

6-4: Standard Form Your Turn Write y = -2/5 x + 1 in standard form 2x + 5y = 5

6-4: Standard Form Assignment Worksheet #6-4 1 – 31, odd problems