Question

How do you find the x and y intercept of \[2x + y = 14\]?

Answer 1

Hint: x-intercept can be found by substituting the value of ‘y’ is equal to zero in the given equation. Similarly we can find the y-intercept by substituting the value of ‘x’ equal to zero in the given equation. In other words ‘x’ intercept is defined as a line or a curve that crosses the x-axis of a graph and ‘y’ intercept is defined as a line or a curve crosses the y-axis of a graph.

Complete step-by-step solution:
Given, \[2x + y = 14\].
To find the ‘x’ intercept put \[y = 0\] in the above equation,
\[\Rightarrow 2x + (0) = 14\]
\[\Rightarrow 2x = 14\]
Divide by 2 on both sides of the equation,
\[\Rightarrow x = \dfrac{{14}}{2}\]
\[ \Rightarrow x = 7\].
Thus ‘x’ intercept is 7.
To find the ‘y’ intercept put \[x = 0\] in the above equation,
\[\Rightarrow 2(0) + y = 14\]
\[ \Rightarrow y = 14\]
Thus ‘y’ intercept is 14.
If we draw the graph for the above equation. We will have a line or curve that crosses the x-axis at 7 and y-axis at 14.

Note: We can solve this using the standard intercept form. That is the equation of line which cuts off intercepts ‘a’ and ‘b’ respectively from ‘x’ and ‘y’ axis is \[\dfrac{x}{a} + \dfrac{y}{b} = 1\]. We convert the given equation into this form and compare it to the desired result.
Given \[2x + y = 14\]
Now we need 1 on the right hand side of the equation, so divide the whole equation by 14. We have,
\[\Rightarrow \dfrac{{2x + y}}{{14}} = \dfrac{{14}}{{14}}\]
Splitting the terms we have,
\[\Rightarrow \dfrac{{2x}}{{14}} + \dfrac{y}{{14}} = \dfrac{{14}}{{14}}\]
That is we have,
\[ \Rightarrow \dfrac{x}{7} + \dfrac{y}{{14}} = 1\]. On comparing with standard intercept form we have ‘x’ intercept is 7 and y intercept is 14. In both the cases we have the same answer.