To determine the y-intercept of the line given by the equation [tex]\( y = -10x + 14 \)[/tex], follow these steps:
1. Understand the y-intercept: The y-intercept is the point where the line crosses the y-axis. This occurs where [tex]\( x \)[/tex] is equal to 0.
2. Set [tex]\( x \)[/tex] to 0 in the equation: Substitute [tex]\( x = 0 \)[/tex] into the equation [tex]\( y = -10x + 14 \)[/tex].
[tex]\[
y = -10(0) + 14
\][/tex]
3. Calculate the value of [tex]\( y \)[/tex]:
[tex]\[
y = 0 + 14
\][/tex]
[tex]\[
y = 14
\][/tex]
4. Determine the y-intercept point: Since the y-intercept is where [tex]\( x = 0 \)[/tex], and we have found [tex]\( y = 14 \)[/tex], the y-intercept is the point [tex]\((0, 14)\)[/tex].
Thus, the y-intercept of the line [tex]\( y = -10x + 14 \)[/tex] is:
[tex]\[ \boxed{(0, 14)} \][/tex]
