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.