Question

The time and distance travelled by a cyclist is given below in the graph. The equation representing the straight line is

• A. y = 2x + 3
• B. y = x + 4
• C. y = 3x + 2

Answer 1

The correct option is C y = 3x + 2

The points B and C are passing through the line.

Coordinates of B is (1,5)

Coordinates of C is (2,8)


$\text{Subtituting B (1,5) in the equation}$
$y=2x+3\text{, we get:}$
$y=2\times 1+3=2+3=5$

The equation of the line y = 2x + 3 satifies the point (1,5)

$\text{Subtituting C (2,8) in the equation}$
$y=2x+3\text{, we get:}$
$y=2\times 2+3=4+3=7$

The equation of the line y = 2x + 3 does not satisfy the point (2,8)

∴ The equation of the line will not pass through (0,2) , (1,5) , (2,8)

$\text{Now, let us substitute B(1,5) in the equation}$
$y=3x+2\text{, we get:}$
$y=3\times 1+2=3+2=5$

The line having the equation y = 3x + 2 passes through the point B(1,5)

Checking the equation for C(2,8), we get:
$y=3x+2=3\times 2+2=6+2=8$

So, the equation of line y = 3x + 2 also satisfy the point C.

∴ The equation of line y = 3x + 2 will satisfy all the three points (0,2) , (1,5) , (2,8)

Finally, let us check the co-ordinates with the line y = x+ 4.

For the point B (1,5) we get:
$y=1+4=5$

For the point C (2,8), we get:
$y=2+4=6$

∴ The equation for the line y = x + 4 does not pass through (0,2) , (1,5) , (2,8)

Hence, the line having the equation y = 3x + 2 passes both through all the points A, B and C.