Question

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.

Answer 1

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.