Question

How do you find the intercepts for \[6x - 3y = - 10\] ?

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, \[6x - 3y = - 10\]. To find the ‘x’ intercept put \[y = 0\] in the above equation,
\[6x - 3(0) = - 10\]
\[\Rightarrow 6x = - 10\]
Divide by 6 on both sides of the equation,
\[x = \dfrac{{ - 10}}{6}\]
\[\Rightarrow x = \dfrac{{ - 5}}{3}\]
\[\Rightarrow x = - 1.666\]
Rounding off we have,
\[ x = - 1.67\].
Thus ‘x’ intercept is \[ - 1.67\].

To find the ‘y’ intercept put \[x = 0\] in the above equation,
\[6(0) - 3y = - 10\]
\[ - 3y = - 10\]
Divide by \[ - 3\] on both sides of the equation,
\[y = \dfrac{{ - 10}}{{ - 3}}\]
\[\therefore y = 3.333\]
Rounding off we have,
\[ \Rightarrow y = 3.33\].
Thus ‘y’ intercept is 3.33. If we draw the graph for the above equation. We will have a line or curve that crosses the x-axis at \[ - 1.67\] and y-axis at 3.33.

Hence,‘x’ intercept is \[ - 1.67\] and ‘y’ intercept is 3.33.

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 \[6x - 3y = - 10\]
Now we need 1 on the right hand side of the equation, so divide the whole equation by -10. We have,
\[\dfrac{{6x - 3y}}{{ - 10}} = \dfrac{{ - 10}}{{ - 10}}\]
Splitting the terms we have,
\[\dfrac{{6x}}{{ - 10}} + \dfrac{{ - 3y}}{{ - 10}} = 1\]
That is we have,
\[\dfrac{x}{{ - 1.67}} + \dfrac{y}{{3.33}} = 1\]
On comparing with standard intercept form we have ‘x’ intercept is \[ - 1.67\] and y intercept is 3.33. In both the cases we have the same answer.