First slide

Equation of line in Straight lines

Question

If the x-intercept of the line $y = mx + 2$ is greater than 1 /2, then the gradient of the line lies in the interval

Moderate

A

$(- 1, 0)$
B

$(\frac{- 1}{4}, 0)$
C

$(- \infty, - 4)$
D

$(- 4, 0)$

Solution

Given equation of line is $y = mx + 2$
$\Rightarrow \frac{x}{- \frac{2}{m}} + \frac{y}{2} = 1$
it is given that x-intercept of the above line is greater than $\frac{1}{2}$
$∴ - \frac{2}{m} - \frac{1}{2} > 0$
$\Rightarrow - \frac{2}{m} - \frac{1}{2} > 0$
$\Rightarrow - (\frac{4 + m}{2 m}) > 0$
$\Rightarrow \frac{4 + m}{2 m} < 0$
$\Rightarrow - 4 < m < 0$

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