graph the equation 9 - x = 3/2y using slope-intercept form.

Answer 1

To graph the equation 9 - x = 3/2y in slope-intercept form, we need to isolate y on one side of the equation by solving for y.

First, let's rewrite the equation in the form y = mx + b, where m is the slope and b is the y-intercept.

9 - x = (3/2)y
To isolate y, divide both sides by (3/2):
(9 - x) / (3/2) = y
Multiplying by the reciprocal:
y = 2/3(9 - x)
y = 2/3(9) - 2/3(x)
y = 6 - 2/3x
y = -2/3x + 6

Now we can identify the slope and y-intercept. The slope is -2/3 and the y-intercept is 6.

To graph the equation, start by plotting the y-intercept at (0,6). Then use the slope to find another point on the line. Since the slope is -2/3, it means that for every 3 units to the right, we go down 2 units. So from the y-intercept (0,6), move 3 units to the right and then 2 units down to plot another point.

Connect the two points with a straight line to graph the equation y = -2/3x + 6.