Question

Draw the graph of the equation x − y = 4

Answer the following using graph paper:
(i) Find the value of y, if x = 7 from the graph.
(ii) Write the coordinate of the point where the graph intersect on x − axis.

Answer 1

We have the equation:

x - y = 4

We can write this as a linear equation in the slope-intercept form if we isolate the variable y.

We get:

y = x - 4

Now to graph this function, we need to evaluate x in two different points and get two points (x, y) of the line.

If we use x = 1 and x = 2, then we get:

y(1) = 1 - 4 = - 3

Then we have the point (1, -3)

and:

y(2) = 2 - 4 = - 2

Then we have the point (2, - 4)

Now we need to draw these two points in the coordinate axis, and draw a line that connects the points, the example can be seen in the image below.

a) To use the graph, we need to locate the value x= 7 in the x-axis.

Then draw a vertical line

In the point where the vertical line intersects the graph, we draw an horizontal line.

The y-value will be the value at which this horizontal line intersects the y-axis

In this case, is at y = 3.

Then when x = 7, y = 3.

(you can see it in the graph)

ii) The coordinate at which the graph intersects the x-axis can be seen in the graph, it is the point (0, 4)