Question

How do you graph the line $y = 3$?

Answer 1

In the above question, we need to plot the above line on the graph. Since, the given equation is a line where the equation of the straight line is $y = mx + c$so we can compare with this equation and find out the coordinates of the line on the cartesian plane.

Complete step by step solution:
In the above equation, we have to plot the line on the graph. To find the coordinates of the line what we can do is to select some values of x coordinate and then evaluate those values in the given equation where we get $y = 3$.
So, first we will select a value for $x$, for example zero and we substitute the value in $y = mx + c$.
where m is the slope of the equation and c is the constant term y-intercept. So, substitute the value in equation we get,
$y = m \times 0 + c$
Since the value of y should be -2, we use m=0 because whatever value we put for x will not matter as long as m=0.
Therefore, the value is $y = 3$,so c value becomes 3. Here c is the y-intercept means the line cutting the y-axis a t point 3.

Therefore, the line is parallel to the x-axis because the value of slope is 0. Since it has no slope the line is in horizontal direction cutting the y-axis at point 3.

Note: An important thing to note is that slope contains the direction in which how you go from one point to another where $m = \dfrac{y}{x} = \dfrac{{rise}}{{run}}$.The numerator tells you much steps to go up and down and the denominator tells us how many steps to move left or right.