Question

What is the slope and intercept for y=9?

Answer 1

Hint: We need to find the slope and intercept of the line y=9. We start to solve the given question by plotting the graph of the line y=9. Then, we find the slope of the given line using the slope formula given by $\dfrac{{{y}_{2}}-{{y}_{1}}}{{{x}_{2}}-{{x}_{1}}}$ to get the desired result.

Complete step-by-step solution:
We are given a line equation and are asked to find the slope of the given line equation. We will be solving the given question using the slope formula $\dfrac{{{y}_{2}}-{{y}_{1}}}{{{x}_{2}}-{{x}_{1}}}$ .
The slope of a straight line is used to determine the steepness of the line. It is usually the ratio of the amount y increases to the amount x increases.
The slope of the line is usually denoted by a variable m.
It is given as follows,
$\Rightarrow m=\dfrac{{{y}_{2}}-{{y}_{1}}}{{{x}_{2}}-{{x}_{1}}}$
Here,
$\left( {{x}_{1}},{{y}_{1}} \right),\left( {{x}_{2}},{{y}_{2}} \right)$ are the first and second coordinates in the line.
According to the question,
We need to find the slope of the line y=9.
The graph of the line y=9 is represented as follows,

From the graph,
We observe that the line y=9 does not pass through the horizontal axis or the x-axis.
From the above,
The value of y is always equal to 9 for any values of the horizontal coordinates.
Following the same, we get,
${{y}_{2}}=9$
${{y}_{1}}=9$
${{x}_{1}}={{x}_{1}}$
${{x}_{2}}={{x}_{2}}$
Substituting the above values of coordinates in the slope formula, we get,
$\Rightarrow m=\dfrac{\left( 9-9 \right)}{{{x}_{2}}-{{x}_{1}}}$
Simplifying the above equation, we get,
$\Rightarrow m=\dfrac{0}{{{x}_{2}}-{{x}_{1}}}$
$\therefore m=0$
The slope of the line y=9 is zero.
The y-intercept is the point where the graph of the function crosses the y-axis. The point lies on the y-axis.
Hence, the coordinates of the y-intercept are given by $\left( x,y \right)$ where the value of $x=0$
According to our question,
We need to find the value of the y-intercept of the line
 $\Rightarrow y=9$
From the graph, we know that the graph of the line is crossing the y-axis at the point $A\left( 0,9 \right)$ .
So, the coordinates of the y-intercept are given by $\left( 0,9 \right)$
$\therefore $ The slope of the line y=9 is zero and the intercept is at a point $\left( 0,9 \right)$

Note: The slope of the line can be alternatively found as follows,
The general equation of the straight line is given by $y=mx+c$
Here,
m = slope
Representing the line y=9 in the form of y=mx+c, we get,
$\Rightarrow y=0x+9$
$\therefore y=0x+9$
Comparing the above equation with the standard line equation, the slope of the line y=9 is zero.