Question

Plot the graph for the following equations:
$y=\frac{4}{5}x+3$
$5y=4x+15$
The above lines represents solutions.

• A. zero
• B. one
• C. infinite number of

Answer 1

The correct option is C infinite number of

Given equations are $\text{y}=\frac{4}{5}\text{x}+3$ and $5\text{y}=4\text{x}+15$

Plot the line $\text{y}=\frac{4}{5}\text{x}+3$

At x = 0, y = $\frac{4}{5}\left(0\right)+3$
y = 3
At x = 15, y = $\frac{4}{5}\left(15\right)+3$
y = 15

So, the line passses through the points (0, 3) and (15, 15).

Plot the line $\text{5y}=4\text{x}+15$

At x = 0, 5y = 15
$⟹\text{y}=\frac{15}{5}$
= 3
At x = 15, 5y = 4(15) + 15
$⟹\text{y}=\frac{75}{5}$
= 15

So, the line passses through the points (0, 3) and (15, 15).

The graph for the above is:

Since both equations overlap each other throughout the graph, the equations have infinite number of solutions.