Question

What are the intercepts of the line $ y = 5x - 10 $ ?

Answer 1

Hint: To find the intercepts, first rearrange the terms of the given equation as $ 5x - y = 10 $ and then write the intercept equation of line $ \dfrac{x}{a} + \dfrac{y}{b} = 1 $ . Now, observe both equations and try to bring the given equation similar to the intercept equation.

Complete step by step solution:
In this question, we are given the standard equation of a straight line and we are supposed to find the values of x – intercept and y – intercept.
 $ \Rightarrow y = 5x - 10 $ - - - - - - - (1)
Now, the intercept form is:
 $ \Rightarrow \dfrac{x}{a} + \dfrac{y}{b} = 1 $ - - - - - - - - - (2)
So, therefore we have to arrange the equation (1) similar to equation (2).
Firstly, rearrange the terms of equation (1).
 $ \Rightarrow 5x - y = 10 $ - - - - - - - - (3)
Now, focus on the constant terms in both the equations. The constant term in equation (2) is 1 and the constant term in equation (3) is 10. So, we need to make constant term 1 in equation (3).
For making the constant term 1, divide the whole equation (3) by 10.
 $ \Rightarrow \dfrac{{5x}}{{10}} - \dfrac{y}{{10}} = \dfrac{{10}}{{10}} $
 $ \Rightarrow \dfrac{x}{2} - \dfrac{y}{{10}} = 1 $ - - - - - - - - (4)
Now, we can compare equations (2) and (4).
Comparing equations (2) and (4), we get
 $ a = 2 $ And $ b = - 10 $
Where $ a = x - \operatorname{int} ercept $ and $ b = y - \operatorname{int} ercept $ .
Hence, the intercepts of the line $ y = 5x - 10 $ are found at points $ \left( {2,0} \right) $ and $ \left( {0, - 10} \right) $ .
So, the correct answer is “ $ \left( {2,0} \right) $ and $ \left( {0, - 10} \right) $ .”.

Note: X- intercept is a point on x-axis and the y-coordinate is 0 for x- intercept.
Y – Intercept is a point on y-axis and the x-coordinate is 0 for y-intercept.