Question

How do you graph $y = 3x + 5$ ?

Answer 1

Hint: In this question, we have to graph an equation, the equation given is a linear equation in terms of two variable quantities namely x and y and it. On putting random values of x, we can get random values of y and thus find the coordinates of one of the points lying on the line. To plot the graph of a straight line we must know the coordinates of at least two points lying on the line so we put the value of both x and y zero one by one and then find the value of other variables from the equation of the line. We can obtain the line on the graph by joining these points.

Complete step-by-step answer:
The equation of the line is $y = 3x + 5$
When $x = 0$
$
  y = 3(0) + 5 \\
   \Rightarrow y = 5 \;
 $
The line cuts the y-axis at $(0,5)$ .
When $y = 0$
$
  0 = 3x + 5 \\
   \Rightarrow x = - \dfrac{5}{3} \;
 $
The line cuts the x-axis at the point $( - \dfrac{5}{3},0)$ .
We can trace the line of the equation $y = 3x + 5$ by joining these two points and then extending the obtained line away in the opposite directions.

Note: A graph shows the relation between two variable quantities, it contains two axes perpendicular to each other namely the x-axis and the y-axis. Each variable is measured along one of the axes. To find the equation of a line, we must know the coordinates of at least two of the points lying on the line. We are given the equation of a line in the question so we had to find the coordinates using the given equation.