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 \[\dfrac{x}{a} + \dfrac{y}{b} = 1\], 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
\[\dfrac{x}{{ - 10}} = 1\]
Here, \[ - 10\] is the \[x\]-intercept, and there is no \[y\]-intercept.