Question

Draw a graph for each of the following equations and find the coordinates of the points where the line drawn meets the x-axis and y-axis: ${\displaystyle \frac{2x}{5}+\frac{y}{2}}$ = 1

Answer 1

${\displaystyle \frac{2x}{5}+\frac{y}{2}}$ = 1

⇒ ${\displaystyle \frac{y}{2}=1-\frac{2x}{5}}$

⇒ ${\displaystyle \frac{y}{2}=\frac{5-2x}{5}}$

⇒ y = ${\displaystyle \frac{10-4x}{5}}$

When x = 0, y = ${\displaystyle \frac{10-4\left(0\right)}{5}}$ = 2

When x = 5, y = ${\displaystyle \frac{10-4\left(5\right)}{5}}$ = -2

When x = ${\displaystyle \frac{5}{2},y=\frac{10-4\left(\frac{5}{2}\right)}{5}}$ = 0

x	0	5	${\displaystyle \frac{5}{2}}$
y	2	-2	0

Plotting the points (0, 2), (5, -2) and ${\displaystyle (\frac{5}{2},0)}$, we get a line segment as shown in the figure.

The line meets the x-axis at ${\displaystyle (\frac{5}{2},0)}$ and y-axis at (0, 2).