Question

How do you find the slope and intercept of $x = 4$ ?

Answer 1

We are given a line and asked to find the slope and intercept of the line. To find the slope of the line, recall the formula to find the slope of the line and use this formula to find the slope. To find the intercept, check where the given line intersects the y-axis and x-axis.

Complete step by step solution:
Given, the equation $x = 4$. We are asked to find the slope and intercept of line $x = 4$. The slope of a line passing to two points $\left( {{x_1},{y_1}} \right)$ and $\left( {{x_2},{y_2}} \right)$ is given by,
$m = \dfrac{{{y_2} - {y_1}}}{{{x_2} - {x_1}}}$ …………………(i)
where ${y_2} - {y_1}$ is changed in the y-axis and ${x_2} - {x_1}$ is changed in the x-axis.

We are given $x = 4$ which means for any value of y , x will be always $4$.
Let us take two points $\left( {4,{y_1}} \right)$ and $\left( {4,{y_2}} \right)$.
Here ${x_1} = {x_2} = 4$.
Putting the values of ${x_1}$, ${x_2}$, ${y_1}$ and ${y_2}$ in equation (i) we get,
$m = \dfrac{{{y_2} - {y_1}}}{{4 - 4}}$
$\Rightarrow m = \dfrac{{{y_2} - {y_1}}}{0}$
$\Rightarrow m = \infty$
Therefore, the slope of the given line is infinite. For any value of y, x will always be $4$ which means the line $x = 4$ is parallel to the y-axis.

The intercept is the point where the line intersects y-axis or x-axis. Here the line is parallel to y-axis so it will never intersect y-axis which means there is no y-intercept. The x-intercept will be the point on x-axis where $y = 0$. Here for any value of y, x is $4$ , so the intercept of the line is $\left( {4,0} \right)$.

Hence, the slope of the given line is infinite and the intercept of the given line is $\left( {4,0} \right)$.

Note: Here, the given line was parallel to y-axis but if we were given a line $y = a$ where $a$ is a number, then the line would be parallel to x-axis as for any value of x the value of y would remain the same and in this case there would be no x-intercept. Also remember the slope of line determines the change in y-axis with respect to the change in x-axis.