First slide

Equation of line in Straight lines

Question

If the x-intercept of the line y = mx + 2 is greater than $\frac{1}{2}$ , 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 l/2.
$\begin{array}{ll} ∴ - \frac{2}{m} > \frac{1}{2} \\ \Rightarrow - \frac{2}{m} - \frac{1}{2} > 0 \\ \Rightarrow \frac{4 + m}{2 m} < 0 \\ \Rightarrow - 4 < m < 0 \end{array}$

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