Question

How do you graph $$x=-10$$ using intercepts?

Answer 1

Hint: Here, we need to graph the given line. We will take the abscissa and ordinate 0 to find the intercepts, and use them to draw the graph of the given equation. The abscissa of a point $$\left(x,y\right)$$ is $$x$$, and the ordinate of a point $$\left(x,y\right)$$ is $$y$$.

Complete step-by-step solution:
First, we will find the intercepts of the given line.
Rewriting the equation, we get
$$x+0\times y=-10$$
Substituting 0 for $$y$$ in the equation, we get
$$x+0\times 0=-10$$
Therefore, we get
$$x=-10$$
The $$x$$-intercept of the given line is $$-10$$.
This means that the line touches the $$x$$-axis at the point $$\left(-10,0\right)$$.
Substituting 0 for $$x$$ in the equation, we get
$$0+0\times y=-10$$
Therefore, we get
$$0=-10$$
This is incorrect.
The given line has no $$y$$-intercept.
Therefore, there is no point on the given line that has the abscissa 0.
This means that the line does not touch the $$y$$-axis at any point.
When two straight lines do not touch each other at any point, they are called parallel lines.
This means that the graph of the line $$x=-10$$ is parallel to the $$y$$-axis.
Now, we will draw the graph of the given line.
The graph of the line $$x=-10$$ touches the $$x$$-axis at the point $$\left(-10,0\right)$$, and is parallel to the $$y$$-axis.
The value of $$x$$ remains $$-10$$ for all values of $$y$$.
Drawing the graph of the line $$x=-10$$, we get

This is the required graph of the line $$x=-10$$.

Note:
We can also rewrite the equation using the intercept form of a line.
The intercept form of a line is given by $${\displaystyle \frac{x}{a}}+{\displaystyle \frac{y}{b}}=1$$, where $$a$$ and $$b$$ are the $$x$$-intercept and $$y$$-intercept cut by the straight line respectively.
Dividing both sides of the given equation by $$-10$$, we get
$${\displaystyle \frac{x}{-10}}=1$$
Here, $$-10$$ is the $$x$$-intercept, and there is no $$y$$-intercept.