High School

Find the [tex]x[/tex] and [tex]y[/tex] intercepts of the equation:

[tex]3x + 5y = 60[/tex]

The intercepts are:

[tex]x[/tex] intercept: [tex]\left( \frac{60}{3}, 0 \right)[/tex]

[tex]y[/tex] intercept: [tex]\left( 0, \frac{60}{5} \right)[/tex]

Answer :

To determine the [tex]\(x\)[/tex] and [tex]\(y\)[/tex] intercepts of the equation [tex]\(3x + 5y = 60\)[/tex]:

### Finding the [tex]\(x\)[/tex]-intercept:
The [tex]\(x\)[/tex]-intercept is the point where the graph of the equation crosses the [tex]\(x\)[/tex]-axis. At this point, the value of [tex]\(y\)[/tex] is 0.

1. Substitute [tex]\(y = 0\)[/tex] into the equation [tex]\(3x + 5y = 60\)[/tex]:
[tex]\[
3x + 5(0) = 60
\][/tex]
2. Simplify the equation:
[tex]\[
3x = 60
\][/tex]
3. Solve for [tex]\(x\)[/tex] by dividing both sides of the equation by 3:
[tex]\[
x = \frac{60}{3}
\][/tex]
[tex]\[
x = 20
\][/tex]

So, the [tex]\(x\)[/tex]-intercept is [tex]\(20\)[/tex].

### Finding the [tex]\(y\)[/tex]-intercept:
The [tex]\(y\)[/tex]-intercept is the point where the graph of the equation crosses the [tex]\(y\)[/tex]-axis. At this point, the value of [tex]\(x\)[/tex] is 0.

1. Substitute [tex]\(x = 0\)[/tex] into the equation [tex]\(3x + 5y = 60\)[/tex]:
[tex]\[
3(0) + 5y = 60
\][/tex]
2. Simplify the equation:
[tex]\[
5y = 60
\][/tex]
3. Solve for [tex]\(y\)[/tex] by dividing both sides of the equation by 5:
[tex]\[
y = \frac{60}{5}
\][/tex]
[tex]\[
y = 12
\][/tex]

So, the [tex]\(y\)[/tex]-intercept is [tex]\(12\)[/tex].

### Conclusion:
- The [tex]\(x\)[/tex]-intercept is [tex]\(20\)[/tex].
- The [tex]\(y\)[/tex]-intercept is [tex]\(12\)[/tex].

Thus, the intercepts of the equation [tex]\(3x + 5y = 60\)[/tex] are [tex]\(x = 20\)[/tex] and [tex]\(y = 12\)[/tex].

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