Put the following equation of a line into slope-intercept form, simplifying all fractions.
2, x, minus, 3, y, equals, minus, 9
2x−3y=
−9
The slope-intercept form of a line is y = mx + b, where m is the slope and b is the y-intercept.
To put the equation 2x - 3y = -9 into slope-intercept form, we need to solve for y:
First, isolate the term containing 'y' on one side of the equation by moving the '2x' term to the other side. To do this, subtract 2x from both sides of the equation:
2x - 3y - 2x = -9 - 2x
This simplifies to:
-3y = -2x - 9
Now we want to solve for y, which means we need to get y by itself. To do this, divide both sides of the equation by -3 to isolate y:
(-3y) / -3 = (-2x - 9) / -3
Simplifying the right side of the equation by dividing each term by -3, we get:
y = (2/3)x + 3
This is the slope-intercept form of the line where the slope (m) is 2/3, and the y-intercept (b) is 3.