Integrated Algebra
NOTES: Isolating y Name
TRANSFORMING EQUATIONS INTO THE SLOPE INTERCEPT FORM
Isolating y ----- Solve for y ----- In terms of y
What is the slope intercept form of a linear equation? ______
What variable is isolated? ______
Linear equations are not always written in the slope intercept form. The standard form for a linear equation is ax + by = c. The x and y terms are on the same side of the equal sign. One way to graph is to transform the equation into y = mx + b form.
EX: Write the equation 10x - 5y = -20 in the slope intercept form.
10x - 5y = -20
-10x -10x subtract 10x from both sides of the equation
-5y = -10x - 20
-5 -5 -5 divide each term by -5
y = 2x + 4
EX: Write the equation 4x + 3y = 24 in the slope intercept form.
4x = 3y + 24 subtract 24 from both sides of the equation
- 24 - 24
4x – 24 = 3y
3 3 3 divide each term by 3
x - 8 = y or y = x - 8
EX: Write the equation - 5y = 2x + 10 in the slope intercept form.
-5y = 2x + 10
-5y = -2x + 10 divide each term by -5
-5 -5 -5
y = x – 2
Translate each of the equations into the slope intercept form. (Isolate the y)
1. 6x + 3y = 6 2. -2x + y = 8
3. x - 4y = 8 4. 3x - y = 5
5. 7y + 14 = 2x 6. 4y = x
7. 3x = 9y - 9 8. 10 = -2y + 2x
9. 2x + y = 0 10. 3x + 6y = 12
Homework Isolating y Name
Isolate y in the following equations;
1. 3x + 5y = 10 2. x = y – 5
3. y + x = 2 4. 8 + x = 2y
5. = x – 3 6. –y = 4x + 1
Graph the following equations. Be sure to put the equation in slope intercept form first.
7. 2x + y = 6 8. 3y = 2x - 3