Question

Given the equation : 2x + 3y = 6
- tell the slope , graph the equation , tell the slope of the line parallel to x + 3y = 6 ..
can anyone tell me how I can do this ?!

Answer 1

First, we'll need to put the equation in the form y = mx + b, where m is the slope and b is the y-intercept (where the line crosses the y-axis).

So first, move the 2x to the right side of the equation, so 2x + 3y = 6 becomes 3y = -2x + 6.

Then, divide through by 3. So y = -2/3 x + 2.

In the form y = mx + b, the slope is represented by m. In this equation, that's -2/3. So the slope is -2/3.

Answer 2

The easiest point to start with when graphing is the y-intercept. The y-intercept is represented by b in the form y = mx + b, so in our equation, that's 2! The x-coordinate of the y-intercept is always 0. So start with the point (0, 2).

Answer 3

Next, you'll need another point to make graphing easier. Try the x-intercept.

y = -2/3 x + 2

Let y = 0.

0 = -2/3 x + 2
-2 = -2/3 x
6 = 2x
x = 3

So (3, 0) is another point you can use.



Your graph should look a little like this! You can pick any x and find the corresponding y and use that as another point if you'd like, to make your graph even more accurate.