3. Graph the equation. − 1 2x− 2 3y= 3 4 *Hint: Find a common multiple of 2, 3, and 4 to cancel out the denominators. *Hint: Find the x-intercept (what is x when y = 0?) and y-intercept (what is y when x = 0?)
To graph the equation − 1/2x− 2/3y= 3/4, we can first clear the denominators by multiplying the entire equation by the common multiple of 2, 3, and 4 which is 12.
12*(-1/2x)- 12*(2/3y)= 12*(3/4)
This simplifies to:
-6x - 8y = 9
To find the x-intercept, let y = 0 and solve for x:
-6x - 8(0) = 9
-6x = 9
x = -9/6
Simplifying further, we get:
x = -3/2
Therefore, the x-intercept is -3/2 or -1.5.
To find the y-intercept, let x = 0 and solve for y:
-6(0) - 8y = 9
-8y = 9
y = -9/8
Therefore, the y-intercept is -9/8 or -1.125.
Plotting these two points (-1.5, 0) and (0, -1.125) on a graph and drawing a line passing through them will give us the graph of the equation -6x - 8y = 9.