Question

How would you draw the graph of the equation \[y = 4\] using slope intercept form?

Answer 1

Hint: In this problem we have to use the slope-intercept form of a straight line to construct the graph. The slope intercept form of a line consists of two important information regarding a line: the slope and the y-intercept. The y intercept is the length at which the line cuts the y-axis and the slope is the angle which the line makes with the x-axis. With this information we can construct the graph.

Complete step-by-step answer:
The slope intercept form of a straight line is represented by: \[y = mx + c\] ; where m is the slope of the straight line and the constant(c) is the y-intercept. Now the task is to represent the equation \[y = 4\] in this form. We can write \[y = 4\] in the following form:
 \[y = 4\] \[ \Rightarrow \,y = 0 \times x\, + 4\]
In this form of equation 0 is the slope of the straight line and 4 is the value of y-intercept. This equation represents that the line \[y = 4\] is parallel to the x-axis as its slope is 0 and the line cuts the y-axis at 4 units in the positive direction. So, we can construct the graph of the given equation in the following manner.

The above graph is the representation of the equation \[y = 4\] .

Note: The slope intercept form of a straight line in general is represented by \[y = \pm mx \pm c\] . The slope of the line may be positive or negative and the same goes for the y-intercept. If the slope is positive, it makes an acute angle with positive x-axis, if it is negative, it makes an acute angle with negative x-axis. If the slope is positive, then the line cuts the y-axis in the positive half and if it's negative it cuts the y-axis in the negative half. The slope and y-intercept determines the orientation of the straight line. The slope-intercept is the most conventional method of expressing a straight line.