Question

Draw graph for equation given below:

`1/2 x + 2/3 y = 5`

Answer 1

To draw the graph of the linear equation `1/2 x + 2/3 y = 5`, it is easiest to find the x-intercept and y-intercept and then connect them with a straight line.

1. Find the intercepts

x-interxept: Set y = 0.

`1/2 x + 2/3 (0) = 5`

⇒ `1/2 x = 5`

⇒ x = 10

The x-intercept is at (10, 0).

y-interxept: Set x = 0.

`1/2 (0) + 2/3 y = 5`

⇒ `2/3 y = 5`

⇒ `y = 15/2`

⇒ y = 7.5

The y-intercept is at (0, 7.5).

2. Solve for y (Slope-Intercept Form)

To plot more points or determine the slope, we can rewrite the equation in y = mx + b form:

`2/3 y = -1/2 x + 5`

`y = 3/2 (-1/2 x + 5)`

`y = -3/4 x + 7.5`

The slope (m) is `-3/4`, meaning for every 4 units the line moves to the right, it moves 3 units down.