Certainly! To find the X-intercept and Y-intercept of the equation [tex]\(3x + 2y = 7\)[/tex], follow these steps:
### Finding the X-intercept:
1. Set [tex]\(y = 0\)[/tex] in the equation to find the X-intercept.
2. Substituting [tex]\(y = 0\)[/tex] into the equation:
[tex]\[
3x + 2(0) = 7
\][/tex]
3. This simplifies to:
[tex]\[
3x = 7
\][/tex]
4. Solve for [tex]\(x\)[/tex]:
[tex]\[
x = \frac{7}{3}
\][/tex]
5. The X-intercept is [tex]\(\frac{7}{3}\)[/tex].
### Finding the Y-intercept:
1. Set [tex]\(x = 0\)[/tex] in the equation to find the Y-intercept.
2. Substituting [tex]\(x = 0\)[/tex] into the equation:
[tex]\[
3(0) + 2y = 7
\][/tex]
3. This simplifies to:
[tex]\[
2y = 7
\][/tex]
4. Solve for [tex]\(y\)[/tex]:
[tex]\[
y = \frac{7}{2}
\][/tex]
5. The Y-intercept is [tex]\(\frac{7}{2}\)[/tex].
Now we can state the intercepts:
- The X-intercept is [tex]\(\frac{7}{3}\)[/tex], which is approximately [tex]\(2.3333333333333335\)[/tex].
- The Y-intercept is [tex]\(\frac{7}{2}\)[/tex], which is [tex]\(3.5\)[/tex].
So, the solution is:
(a) X-intercept is [tex]\(\frac{7}{3}\)[/tex]
(d) Y-intercept is [tex]\(\frac{7}{2}\)[/tex]
