Question

How do you graph $ y = - 2x + 7 $ by plotting points?

Answer 1

Hint: In this question, we have to plot a linear equation in terms of two variables on the graph paper by plotting points. For graphing an equation by plotting points, we have to find the coordinates of at least two points lying on the line. As the equation is linear in terms of two unknown variables, that is, x and y so by putting random values of one variable we can find the value of the other value from the given equation. Using this approach, we find out the coordinates of two points lying on the line and get the graph of the line by joining these points.

Complete step-by-step answer:
The equation of the line is \[y = - 2x + 7\]
When $ x = 0 $
 $
  y = - 2(0) + 7 \\
   \Rightarrow y = 7 \;
  $
The line cuts the y-axis at the point $ (0,7) $
When $ y = 0 $
\[
  0 = - 2x + 7 \\
   \Rightarrow 2x = 7 \\
   \Rightarrow x = \dfrac{7}{2} \;
 \]
The line cuts the x-axis at the point $ (\dfrac{7}{2},0) $
Joining these two points and extending the obtained line away in the opposite directions, we can trace the line of the equation \[y = - 2x + 7\] .

Note: We use a graph to study the relation between two variable quantities, a graph contains two axes that are perpendicular to each other namely the x-axis and the y-axis. Instead of putting random values of the unknown quantity, we first put the value of x as zero and get the value of y, and then we put the value y as zero and get the value of x because the obtained points are more convenient and easier to plot on the graph.