Question

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

Answer 1

Hint:Here 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, \[3x + 4y = - 4\]. To find the ‘x’ intercept put \[y = 0\] in the above equation,
\[3x + 4(0) = - 4\]
\[\Rightarrow 3x = - 4\]
Divide by 3 on both sides of the equation,
\[x = \dfrac{{ - 4}}{3}\]
\[\Rightarrow x = - 1.333\]
Rounding off we have,
\[ x = - 1.33\].
Thus ‘x’ intercept is \[ - 1.33\].

To find the ‘y’ intercept put \[x = 0\] in the above equation,
\[3(0) + 4y = - 4\]
\[\Rightarrow 4y = - 4\]
Divide by 4 on both sides of the equation,
\[y = \dfrac{{ - 4}}{4}\]
\[ \Rightarrow y = - 1\].
Thus ‘y’ intercept is -1. If we draw the graph for the above equation. We will have a line or curve that crosses the x-axis at \[ - 1.33\] and y-axis at -1.

Hence, ‘x’ intercept is \[ - 1.33\] and ‘y’ intercept is -1.

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 \[3x + 4y = - 4\]
Now we need 1 on the right hand side of the equation, so divide the whole equation by -4. We have,
\[\dfrac{{3x + 4y}}{{ - 4}} = \dfrac{{ - 4}}{{ - 4}}\]
Splitting the terms we have,
\[\dfrac{{3x}}{{ - 4}} + \dfrac{{4y}}{{ - 4}} = 1\]
That is we have,
\[\dfrac{x}{{ - 1.33}} + \dfrac{y}{{ - 1}} = 1\]
On comparing with standard intercept form we have ‘x’ intercept is \[ - 1.33\] and y intercept is -1. In both the cases we have the same answer.