Question

Draw the graph of equation 5x + 4y = 20. Use the graph drawn to find:

1. x₁, the value of x, when y = 10.
2. y₁, the value of y, when x = 8.

Answer 1

To plot the graph of the linear equation 5x + 4y = 20, we find its intercepts with the axes and then use the graph to determine specific values of x and y.

1. Determining the intercepts

To draw a straight line, we need at least two points. The easiest points to find are the x and y intercepts:

x-intercept: Set y = 0 in the equation:

5x + 4(0) = 20

⇒ 5x = 20

⇒ x = 4

The x-intercept is at (4, 0).

y-intercept: Set x = 0 in the equation:

5(0) + 4y = 20

⇒ 4y = 20

⇒ y = 5

The y-intercept is at (0, 5).

2. Graph of 5x + 4y = 20

Plot these two points on a cartesian plane and draw a straight line through them.

3. Finding specific values from the graph

Using the line drawn, we can find the required values:

i. Value of x₁ when y = 10:

Look at the y-axis at 10 and move horizontally to the line. From that point, move downtothe x-axis.

Mathematically: 5x + 4(10) = 20

⇒ 5x + 40 = 20

⇒ 5x = –20

⇒ x = –4

So, x₁ = –4.

ii. Value of y₁ when x = 8: 

Look at the x-axis at 8 and move vertically to the line. From that point, move across to the y-axis.

Mathematically: 5(8) + 4y = 20

⇒ 40 + 4y = 20

⇒ 4y = –20

⇒ y = –5

So, y₁ = –5.