Put the following equation of a line into slope-intercept form, simplifying all fractions. 5x+6y= 6

Answer 1

Slope-intercept form is y = mx + b where m is the slope of the line and b is the y-coordinate of the y-intercept.

To place the given equation in standard form you need to isolate the y variable. Start by subtracting the term 5x from both sides (subtraction property for equality). Another way to think about moving the term 5x to the other side of the equal sign is to picture "dragging" it to the other side and changing its sign. This is also called transposing a term. The result:

6y = -5x + 6

To finish isolating y, divide every term of the equation by 6 (the coefficient of y).

y = (-5/6)x + 6/6 or y = (-5/6)x + 1

The y-intercept is located at (0,1). The slope is -5/6, which means a run of 6 followed by a rise of -5. You can also think of -5/6 as 5/-6 (run of -6 then a rise of 5. As you move from left to right on the coordinate plane this line slopes "downhill" (negative slope).

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