Question

How do you find the slope and y-intercept for the line $y = 4?$

Answer 1

in this question we have line $y = 4$, which means the line is horizontal. And if the line is horizontal, the slope will become zero. And also the line is crossing the point at $(0,4)$ therefore the y-intercept is $4$.

Complete step by step answer:
Standard form of any line is $y = mx + b$
Where m is slope and b is the y-intercept.
The slope of the line when two points on the line are given:
$m = \dfrac{{{y_2} - {y_1}}}{{{x_2} - {x_1}}}$
$({x_1},{y_1})$ and $({x_2},{y_2})$ are points on line
Here, line is $y = 4$ therefor all y-coordinate are the same
So ${y_2} = {y_1}$, and because of that slope of the line will become zero.
The y-intercept of the line when two points on the line are given:
$b = \dfrac{{{x_2}{y_1} - {x_1}{y_2}}}{{{x_2} - {x_1}}}$
$({x_1},{y_1})$ and $({x_2},{y_2})$ are points on line
Here, the line is horizontal and for horizontal line the y-intercept will be equal to y-coordinate of the given line.
So, the y-intercept $b = 4$
Here, the answer to this question is given below:
The slope for the line $y = 4$ is zero.
The y-intercept for the line $y = 4$ is $4$.

Note:
There are two special cases of lines:
$1st$ Horizontal lines, in the value of this line of y-coordinate, is always the same,
So ${y_1} = {y_2}$ and slope of a horizontal line is $0$.
$2nd$ Vertical lines, in this lines values of x- coordinate is always the same,
So ${x_2} = {x_1}$ and slope of a vertical line is undefined.