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Graphing linear equations Part One Solving for Y In order to graph a linear equation you must first solve for y. Given the Problem : First check to see if y is + or –. x+y=4 If y is + you leave it alone. What number or factor is on the same side of the equation as + y? x+y=4 Move that number or factor to the other side of the = and change its sign. x+y=4 Move that number or factor to the other side of the = and change its sign. y=4-x Your answer is: y=4-x Given the Problem : First check to see if y is + or –. x-y=4 If y is - you move y to the other side of the = and change it to +y. What number or factor is on the same side of the equation as + y? x=4+y Move that number or factor to the other side of the = and change its sign. x=4+y Your answer is: x-4 =y or y=x-4 Given the Problem : x+2y=4 First check to see if y is + or –. x+2y=4 If y is + you leave it alone. What number or factor is on the same side of the equation as + y? x+2y=4 Move that number or factor to the other side of the = and change its sign. x+2y=4 Move that number or factor to the other side of the = and change its sign. 2y=4-x If the +y factor has a co-efficient it must lose it. The factors and numbers on the opposite side of the = become a fraction with the y coefficient as the denominator. 2y=4-x If the +y factor has a co-efficient it must lose it. The factors and numbers on the opposite side of the = become a fraction with the y coefficient as the denominator. 4x y 2 Given the Problem : 2x-2y=4 First check to see if y is + or –. 2x-2y=4 If y is - you move y to the other side of the = and change it to +y. 2x-2y=4 2x=4+2y What number or factor is on the same side of the equation as + y? 2x=4+2y Move that number or factor to the other side of the = and change its sign. 2x=4+2y 2x-4 =2y Your answer is: 2x-4 =2y or 2y=2x-4 If the +y factor has a co-efficient it must lose it. The factors and numbers on the opposite side of the = become a fraction with the y coefficient as the denominator. 2y=2x-4 If the +y factor has a co-efficient it must lose it. The factors and numbers on the opposite side of the = become a fraction with the y coefficient as the denominator. 2x 4 y 2 Advanced Level • There are times when it will be necessary to work the equation to a simpler level. • For example the formula for slope intercept is y = mx + b. Any denominator in this case must be eliminated. How to do this? Most often when we think of the distributive property, we are thinking of using it with ( ) and the operation is multiplication. 2x 4 In the previous example y 2 the line is also a grouping tool with the operation division. 2x 4 y 2 2x 4 y 2 2 y x2 This is a more complex problem. x4 y 2 x 4 y 2 x 4 y 2 2 Y=(1/2)x - 2