Question

How do you find the intercepts for \[4x - 3y = 24\] ?

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, \[4x - 3y = 24\]. To find the ‘x’ intercept put \[y = 0\] in the above equation,
\[4x - 3(0) = 24\]
\[4x = 24\]
Divide by 4 on both sides of the equation,
\[x = \dfrac{{24}}{4}\]
\[ \Rightarrow x = 6\].
Thus ‘x’ intercept is 6.

To find the ‘y’ intercept put \[x = 0\] in the above equation,
\[4(0) - 3y = 24\]
\[ \Rightarrow - 3y = 24\]
Divide by \[ - 3\] on both sides of the equation,
\[y = \dfrac{{24}}{{ - 3}}\]
\[ \Rightarrow y = - 8\].
Thus ‘y’ intercept is \[ - 8\]. If we draw the graph for the above equation. We will have a line or curve that crosses x-axis at 6 and y-axis at \[ - 8\].

Hence, ‘x’ intercept is 6 and ‘y’ intercept is \[ - 8\].

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 \[4x - 3y = 24\]
Now we need 1 on the right hand side of the equation, so divide the whole equation by 24. We have,
\[\dfrac{{4x - 3y}}{{24}} = \dfrac{{24}}{{24}}\]
Splitting the terms we have,
\[\dfrac{{4x}}{{24}} + \dfrac{{ - 3y}}{{24}} = \dfrac{{24}}{{24}}\]
That is we have,
\[\dfrac{x}{6} + \dfrac{y}{{ - 8}} = 1\]
On comparing with standard intercept form we have ‘x’ intercept is 6 and y intercept is -8. In both the cases we have the same answer.