Question

What is the y – intercept for the straight line 2x – 3y = 5?
A. $\dfrac{2}{5}$
B. $-\dfrac{5}{3}$
C. $-\dfrac{5}{2}$
D. $\dfrac{1}{2}$

Answer 1

Hint: We have to know about the concept of y – intercept for a straight line. It is a point where the straight line intersects the y axis of the coordinate system. We can find the y – intercept of a straight line by satisfying the condition of x = 0 in the equation of the line given.

Complete step-by-step answer:
In this question, we have been asked to find the y – intercept for the straight line 2x – 3y = 5. Before we start solving this question, let us see what the y – intercept of a straight line means. Y – intercept which is also known as the vertical intercept is a point where the straight line intersects the y axis. We can find the y – intercept of a straight line by substituting x = 0 in the equation of the line.
We have been given the equation of the line as 2x – 3y = 5. In order to find the y- intercept, we will put the value x = 0 in the equation of line. So, we get,
2 (0) – 3y = 5
0 – 3y = 5
-3y = 5
On dividing the above equation with -3, we will get,
$\begin{align}
  & \dfrac{-3y}{-3}=\dfrac{5}{-3} \\
 & y=-\dfrac{5}{3} \\
\end{align}$
Therefore, we get the y – intercept of the straight line, 2x – 3y = 5 as $-\dfrac{5}{3}$.
Hence, option (B) is the correct answer.

Note: The most common mistake one can make in this question is by substituting the value of y = 0 in the equation of the line in order to find the y = intercept, but this is wrong as substituting y = 0 will give the x – intercept of the given straight line. And we will get the incorrect answer. Also remember that by substituting x = 0 to any curve, we get the y – intercept and by substituting y = 0 to the curve, we get the x – intercept of that curve.