Question

How do you find the intercept for \[ - 3x - 4y = 18\] ?

Answer 1

Hint:We need to find ‘x’ and ‘y’ intercept. 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, \[ - 3x - 4y = 18\].
To find the ‘x’ intercept put \[y = 0\] in the above equation,
\[ - 3x - 4(0) = 18\]
\[\Rightarrow - 3x = 18\]
Divide by \[ - 3\] on both sides of the equation,
\[x = \dfrac{{18}}{{ - 3}}\]
\[ \Rightarrow x = - 6\].
Thus ‘x’ intercept is \[ - 6\].

To find the ‘y’ intercept put \[x = 0\] in the above equation,
\[ - 3(0) - 4y = 18\]
\[\Rightarrow - 4y = 18\]
Divide by \[ - 4\] on both sides of the equation,
\[y = \dfrac{{18}}{{ - 4}}\]
\[ \Rightarrow y = - 4.5\].
Thus ‘y’ intercept is \[ - 4.5\]. If we draw the graph for the above equation. We will have a line or curve that crosses the x-axis at \[ - 6\] and y-axis at \[ - 4.5\].

Hence,‘x’ intercept is \[ - 6\] and ‘y’ intercept is \[ - 4.5\].

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 \[ - 3x - 4y = 18\]
Now we need 1 on the right hand side of the equation, so divide the whole equation by 18. We have,
\[\dfrac{{ - 3x - 4y}}{{18}} = \dfrac{{18}}{{18}}\]
Splitting the terms we have,
\[\dfrac{{ - 3x}}{{18}} + \dfrac{{ - 4y}}{{18}} = 1\]
That is we have,
\[\dfrac{x}{{ - 6}} + \dfrac{y}{{ - 4.5}} = 1\]
On comparing with standard intercept form we have ‘x’ intercept is \[ - 6\] and y intercept is \[ - 4.5\]. In both the cases we have the same answer.