At what point does the line given by the following equation cross the $y$-axis?
$y=\frac{6}{7} x+3$
A. $(0,3)$
B. $\left(-\frac{9}{2}, 0\right)$
C. $(3,0)$
D. $\left(0,-\frac{9}{2}\right)$
Answer (2)
To find where the line crosses the y -axis, set x = 0 .
Substitute x = 0 into the equation: y = 7 6 ( 0 ) + 3 .
Simplify to find y = 3 .
The line crosses the y -axis at the point ( 0 , 3 ) .
Explanation
Understanding the Problem The problem asks us to find the point where the line y = 7 6 x + 3 crosses the y -axis. This point is also known as the y -intercept.
Finding the y-intercept To find the y -intercept, we need to find the value of y when x = 0 . We substitute x = 0 into the equation of the line: y = 7 6 ( 0 ) + 3
Simplifying the equation Simplifying the equation, we get: y = 0 + 3 y = 3
Stating the Answer Therefore, the line crosses the y -axis at the point ( 0 , 3 ) .
Examples
Understanding where a line crosses the y-axis is useful in many real-world scenarios. For example, if you are tracking the growth of a plant over time, the y-intercept might represent the initial height of the plant when you started tracking it. Similarly, in business, the y-intercept of a cost function could represent the fixed costs that a company has to pay regardless of how much they produce. Knowing the y-intercept gives you a starting point or a baseline for your analysis.
The line crosses the y-axis at the point ( 0 , 3 ) . Therefore, the correct answer is option A: ( 0 , 3 ) .
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