Question

How do you find the $x$ and $y$ intercepts of $6x - y = 7$ ?

Answer 1

Hint : To find the co-ordinates of the intercepts for any axis, the first step we need to do to find either of $x$ and $y$ co-ordinates is to put the value of the other variable as $0$ in the given equation. Then by solving the equation, we will be able to obtain the value of the other variable, through which we can generate an ordered pair which will be the intercept.

Complete step by step solution:
To find the $x$ intercept of this equation, we need to place the value of $y$ as $0$ . Then, we need to find out the value of $x$ for which $6x - y = 7$ is satisfied if $y = 0$ .
Putting $y = 0$ , we get the following.

$$6x = 7 \\\ x = \dfrac{7}{6} \;$$

Thus, for $y = 0$ and $x = \dfrac{7}{6}$ , this equation will be satisfied. Hence, we obtain the $x$ intercept as $\left( {\dfrac{7}{6},0} \right)$ .
Now,
To find the $y$ intercept of this equation, we need to place the value of $x$ as $0$ . Then, we need to find out the value of $y$ for which $6x - y = 7$ is satisfied if $x = 0$ .
Putting $x = 0$ , we get the following.

$$\- y = 7 \\\ y = - 7 \;$$

Thus, for $x = 0$ and $y = - 7$ , this equation will be satisfied. Hence, we obtain the $y$ intercept as $\left( {0, - 7} \right)$ .
So, the correct answer is “ $\left( {\dfrac{7}{6},0} \right)$ and $\left( {0, - 7} \right)$ ”.

Note : The x-intercept is a point on the graph, where the value of y is zero. If a line is parallel to the y-axis, then the x-intercept is not defined. The y-intercept, on the other hand, is a point on the graph where x is zero. If a line is parallel to the x-axis, its y-intercept is not defined, because in the case of lines parallel to an axis, there will be no point of intersection for the axis and the line.