Question

Draw the graph of the straight line given by 2 (x + 1/2) = (5 + y) by converting it into its standard form. Also, calculate the area formed by x = 0, y = 0 and the line drawn.

Answer 1

Step-by-step explanation:

Given:

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

To find:

1)Convert into standard form

2) Draw graph

3) Find the area

formed by x-axis, y-axis and the line

drawn

Solution:

Standard form of linear equation is

$\bold{ax + by + c = 0}$

Thus

$2x + 2 \times \frac{1}{2} = (5 + y) \\ \\ 2x + 1 = 5 + y \\ \\ 2x - y + 1 - 5 = 0 \\ \\\bold{\pink{ 2x - y - 4 = 0 }}$

This is standard form of equation.

2) Graph:

To plot the graph;put different value of x and find different values of y

$\begin{tabular}{|c|c|c|c|}\cline{1-4}x&0&2&3\\\cline{1-4}y&-4&0&2\\\cline{1-4}\end{tabular}$

Now plot these points and join.

Graph is attached.

3) Area formed by line , x-axis and y-axis

Solution:In 4th quadrant,A right triangle is formed with line and both axes

Area of right triangle:

$\frac{1}{2} \times base \times height \\ \\ = \frac{1}{2} \times 2 \times 4 \\ \\ \bold{\red{Area= 4 \: sq.units}}$

Hope it helps you.

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Answer 2

Answer:

area=4 square.units........