Question

How do you find the intercepts for \[4x + 3y = 8\] ?

Answer 1

Hint:Here we need to find ‘x’ and ‘y’ intercepts. 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 answer:
Given, \[4x + 3y = 8\]. To find the ‘x’ intercept put \[y = 0\] in the above equation,
\[4x + 3(0) = 8\]
\[ \Rightarrow 4x = 8\]
Divide by 4 on both sides of the equation,
\[x = \dfrac{8}{4}\]
\[ \Rightarrow x = 2\].
Thus ‘x’ intercept is 2.

To find the ‘y’ intercept put \[x = 0\] in the above equation,
\[4(0) + 3y = 8\]
\[ \Rightarrow 3y = 8\]
Divide by 3 on both sides of the equation,
\[y = \dfrac{8}{3}\]
\[ \Rightarrow y = 2.666\].
Rounding off we have,
\[ y = 2.67\]
Thus ‘y’ intercept is 2.67. If we draw the graph for the above equation. We will have a line or curve that crosses the x-axis at 8 and y-axis at -4.

Hence,‘x’ intercept is 2 and ‘y’ intercept is 2.67.

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 will have a desired result.
Given \[4x + 3y = 8\]
Now we need 1 on the right hand side of the equation, so divide the whole equation by 24. We have,
\[\dfrac{{4x + 3y}}{8} = \dfrac{8}{8}\]
Splitting the terms we have,
\[\dfrac{{4x}}{8} + \dfrac{{3y}}{8} = 1\]
That is we have,
\[\dfrac{x}{2} + \dfrac{y}{{2.67}} = 1\]
On comparing with standard intercept form we have ‘x’ intercept is 2 and y intercept is 2.67. In both the cases we have the same answer.