Graph the equation 9 - x = 3/2 * y using slope-intercept form.
To graph the equation 9 - x = 3/2 * y, we need to rearrange the equation to slope-intercept form, which is y = mx + b, where m represents the slope and b represents the y-intercept.
Let's rearrange the given equation:
9 - x = 3/2 * y
First, isolate y by subtracting 9 from both sides:
-x = 3/2 * y - 9
Next, rearrange the equation so that y is on the left side:
3/2 * y = x - 9
Finally, divide both sides by 3/2 to solve for y:
y = (2/3) * x - 6
Now that the equation is in slope-intercept form, we can identify that m = 2/3 (the coefficient of x) and b = -6 (the constant).
To graph this equation, start by plotting the y-intercept, which is the point (0, -6). Then, use the slope m = 2/3 to determine the rise and run from the y-intercept.
For every 2 units increase in x, y increases by 3 units. For every 2 units decrease in x, y decreases by 3 units.
Start by plotting the y-intercept of (0, -6). Then use the slope m = 2/3 to determine additional points:
For x = 2, y = (2/3)(2) - 6 = -4
For x = -2, y = (2/3)(-2) - 6 = -8
Plot these points and draw a line connecting them.