To find the [tex]\(y\)[/tex]-intercept of the equation [tex]\(2x - 5y = 35\)[/tex], we need to determine the value of [tex]\(y\)[/tex] when [tex]\(x = 0\)[/tex]. Here is the step-by-step process:
1. Substitute [tex]\(x = 0\)[/tex] into the equation:
[tex]\[
2(0) - 5y = 35
\][/tex]
2. Simplify the equation:
[tex]\[
0 - 5y = 35
\][/tex]
[tex]\[
-5y = 35
\][/tex]
3. Solve for [tex]\(y\)[/tex]:
[tex]\[
y = \frac{35}{-5}
\][/tex]
[tex]\[
y = -7
\][/tex]
Therefore, the [tex]\(y\)[/tex]-intercept of the equation [tex]\(2x - 5y = 35\)[/tex] is [tex]\(-7\)[/tex]. This means that the point [tex]\((0, -7)\)[/tex] is where the line crosses the [tex]\(y\)[/tex]-axis.
