Question

Draw graph for equation given below: 

2x – 5y = 10

Answer 1

To graph the linear equation 2x – 5y = 10, we can convert it into slope-intercept form (y = mx + b) or find the intercepts.

1. Find the Intercepts

Finding where the line crosses the axes is the most efficient way to sketch a linear graph.

x-intercept (Set y = 0):

2x – 5(0) = 10

⇒ 2x = 10

⇒ x = 5

The line passes through (5, 0).

y-intercept (Set x = 0):

2(0) – 5y = 10

⇒ –5y = 10

⇒ y = –2

The line passes through (0, –2).

2. Solve for y (Slope-Intercept Form)

We rearrange the equation:

2x – 5y = 10

–5y = –2x + 10

`y = 2/5 x - 2`

Slope (m): `2/5` For every 5 units you move right, you move 2 units up.

y-intercept (b): = –2.

3. Analysis of the graph

The graph is a straight line with a positive slope, meaning it rises from left to right. It crosses the vertical axis at –2 and the horizontal axis at 5.