Using the given equation,
(a) find the intercepts of its graph and
(b) use the intercepts to graph the equation.
5x+3y=15
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Part 1
(a) Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A.
The intercept(s) is/are enter your response here.
(Type an ordered pair. Use a comma to separate answers as needed.)
B.
There are no intercepts.
To find the intercepts of the graph, substitute 0 for x and solve for y to find the y-intercept, and substitute 0 for y and solve for x to find the x-intercept.
(a) To find the y-intercept, let x = 0:
5(0) + 3y = 15
0 + 3y = 15
3y = 15
y = 15/3
y = 5
Thus, the y-intercept is (0,5).
To find the x-intercept, let y = 0:
5x + 3(0) = 15
5x + 0 = 15
5x = 15
x = 15/5
x = 3
Thus, the x-intercept is (3,0).
(a) The intercepts are (0,5) and (3,0).
(b) Now, use the intercepts to graph the equation. Plot the points (0,5) and (3,0) on the coordinate plane and draw a straight line passing through these two points. This will be the graph of the equation 5x + 3y = 15.
To find the intercepts of the graph for the equation 5x+3y=15, we need to set one of the variables to zero and solve for the other variable.
(a) To find the x-intercept:
Setting y = 0, we have:
5x + 3(0) = 15
5x = 15
x = 3
So, the x-intercept is (3, 0).
(b) To find the y-intercept:
Setting x = 0, we have:
5(0) + 3y = 15
3y = 15
y = 5
So, the y-intercept is (0, 5).
Therefore, the intercepts of the graph are (3, 0) and (0, 5).
Now, let's use the intercepts to graph the equation.
Plot the points (3, 0) and (0, 5) on a graph and then connect them with a straight line. This is the graph of the equation 5x+3y=15.
To find the intercepts of the graph, we need to solve the equation for both x-intercept and y-intercept.
For the x-intercept, we set y = 0 and solve for x:
5x + 3(0) = 15
5x = 15
x = 15/5
x = 3
So the x-intercept is (3, 0).
For the y-intercept, we set x = 0 and solve for y:
5(0) + 3y = 15
3y = 15
y = 15/3
y = 5
So the y-intercept is (0, 5).
Therefore, the correct choice for part (a) is A. The intercepts are (3, 0) and (0, 5).