Question

How do you find the x and y intercepts for $ 3x + 2y = 1 $ ?

Answer 1

Hint: Lines crossing on any point on the x-axis and y-axis are called x-intercept and y-intercept respectively. So, in the above question, we need to find out the point on both the axes by using the formula for the equation of straight line $ y = mx + c $ since it is the line that cuts the axis at a point.

Complete step by step answer:
The x-intercept forms when the line crosses the x-axis, so at this point, the y coordinate becomes 0. Similarly, for the y-intercept, the line crosses the x-axis and the x coordinate becomes 0. The below-shown graph is a general example of how to intercept forms.

In the given equation, we need to rearrange the equation in such a way that it should form the general equation of line i.e. y=mx+c where m is the slope of the line and c is the intercept.
\[
  3x + 2y = 1 \\
    \\
 \]
So, we will first find out the y-intercept.
\[
  2y = - 3x + 1 \\
  y = \dfrac{{ - 3x}}{2} + \dfrac{1}{2} \\
 \]
On comparing c in the equation
 \[y = mx + c\] , we get
 \[c = \dfrac{1}{2}\].
So, the above value is of the y-intercept.
Further for finding x-intercept we get,
\[
   \Rightarrow 3x = - 2y + 1 \\
   \Rightarrow x = \dfrac{{ - 2}}{3} + \dfrac{1}{3} \\
 \]
Therefore, the x-intercept is \[\dfrac{1}{3}\] and y-intercept is \[\dfrac{1}{2}\].

Note:
In the above question, an alternative method can be followed by substituting either value of a and y as 0. Suppose we need to find x intercept then we substitute the value of y=0 in the equation\[3x + 2(0) = 1\], then we get the above x-intercept value and we find y-intercept then we substitute the value of x=0 in the equation \[3(0) + 2y = 1\] we get above y-intercept value.