Question

How do you find the $x$ and $y$ intercepts for $y = x - 3$ ?

Answer 1

To solve this question we should know about linear equations.
Linear equation: The equation having the highest power of its variable is one.
General linear equation in standard form is $Ax + By = C$ .
Here, $A,B\,and\,C$ is constant.
Intercept: the point on the number line at which the line is crossed.

Complete step by step solution:
As given in question:
The equation is, $y = x - 3$ .
We have to calculate $x$ and $y$ intercepts for $y = x - 3$ .
To calculate it we will go step by step:
As we know, an intercept is the point at which a given line crosses that line. So, it means the coordinate on the other line will be zero except the line at which intercepts.
Step 1: To calculate $x$ intercepts:
So, we can say when $y = x - 3$ is intercept with the $x - axis$ the $y$ coordinate will be zero.
At $y = 0$ ,
Keeping value in equation we get,
$\Rightarrow 0 = x - 3$
$\Rightarrow x = 3$
Step 2: To calculate $y$ intercepts:
So, we can say when $y = x - 3$ is intercept with $y - axis$ the $x$ coordinate will be zero.
At $x = 0$ ,
Keeping value in equation we get,
$\Rightarrow y = 0 - 3$
$\Rightarrow y = - 3$

Hence, $x\,and\,y$ intercept is $3\,and\, - 3$ respectively.

Note: There are many general form of linear equation:
General form: $Ax + By + C = 0$
Point-slope form: $y - {y_1} = m(x - {x_1})$
Slope intercept form: $y = mx + c$
A linear equation can be obtained by equating to zero a linear polynomial over some field, from which the coefficients are taken. The solution of such an equation are the values that, when substituted for the unknowns, make the equality true.