Question

How do you find the points where the graph of \[2x + y = 8\] intersect at the x and y axis?

Answer 1

Hint: The given equation \[2x + y = 8\] is the equation of a straight line. To find x-intercept of a line, we must substitute $ 0 $ for y in the given equation and solve for x. In the same way, to find the y-intercept of a line, we must substitute $ 0 $ for x in the given equation and solve for y.

Complete step-by-step answer:
The given equation is \[2x + y = 8 - - - (1)\].
We must find the point of intersection at x and y axis.
The graph of the equation \[2x + y = 8\] is given below.

When this line crosses the x axis, the y coordinate will be zero. Hence, we substitute $ y = 0 $ in equation $ (1) $ , to get
 $
  2x + 0 = 8 \\
   \Rightarrow 2x = 8 \;
 $
Dividing by $ 2 $ on both sides we get,
 $
  \dfrac{{2x}}{2} = \dfrac{8}{2} \\
   \Rightarrow x = 4 \;
 $
Thus, we get the point $ (4,0) $ on the x axis.
Similarly, when this same line crosses the y axis, the x coordinate will be zero.
Hence, we substitute $ x = 0 $ in equation $ (1) $ , to get
 $
  2(0) + y = 8 \\
   \Rightarrow 0 + y = 8 \;
 $
(Anything multiplied by zero is zero)
So $ y = 8 $ .
Thus, we get the point $ (0,8) $ on the y axis.
Therefore, we have the points $ (4,0) $ and $ (0,8) $ where the graph of \[2x + y = 8\] intersects.

Note: To draw the graph of the equation \[2x + y = 8\], first we have to find the value of y and then we take the values of x as $ 0,1,2,3,4,.... $ . Substituting these values of x in the equation that we found out for y, we get corresponding values of y. Using those set of coordinate points, we can plot the points to get a straight line graph.