Find the intercepts and graph the equation.
3x+4y=12
intercepts:
what is y when x=0?
what is x when y=0?
graph:
visit wolframalpha.com and enter
plot 3x+4y=12
To find the intercepts and graph the equation 3x + 4y = 12, we need to solve for x and y when the equation is equal to zero, as these values will give us the x-intercept and y-intercept respectively.
1. Finding the x-intercept:
To find the x-intercept, we set y = 0 and solve for x.
When y = 0, the equation becomes:
3x + 4(0) = 12
Simplifying:
3x = 12
Divide both sides of the equation by 3 to solve for x:
x = 12/3
x = 4
So, the x-intercept is (4, 0).
2. Finding the y-intercept:
To find the y-intercept, we set x = 0 and solve for y.
When x = 0, the equation becomes:
3(0) + 4y = 12
Simplifying:
4y = 12
Divide both sides of the equation by 4 to solve for y:
y = 12/4
y = 3
So, the y-intercept is (0, 3).
3. Graphing the equation:
Now that we have the x-intercept (4, 0) and the y-intercept (0, 3), we can plot these two points on a Cartesian plane and draw a straight line passing through them. This line represents the graph of 3x + 4y = 12.
The graph should look something like this:
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So, the intercepts are (4, 0) and (0, 3), and the graph of the equation 3x + 4y = 12 is a straight line passing through those points.