First slide

Equation of line in Straight lines

Question

$Equation of the line passing through the point (5, 7) and having y -intercept 5 is$

Moderate

A

$x - y + 5 = 0$
B

$2 x - y + 5 = 0$
C

$2 x - 5 y + 25 = 0$
D

$2 x - 5 y - 25 = 0$

Solution

$If y -intercept of the line is 5 then the line passing through the point (0, 5)$
$The equation of the line joining two points (x_{1}, y_{1}) and (x_{2}, y_{2}) is y - y_{1} = \frac{y_{2} - y_{1}}{x_{2} - x_{1}} (x - x_{1})$
$Hence the equation of the line joining (5, 7) and (0, 5) is$
$\begin{matrix} y - 7 = \frac{5 - 7}{0 - 5} (x - 5) \\ y - 7 = \frac{2}{5} (x - 5) \\ 5 y - 35 = 2 x - 10 \\ 2 x - 5 y + 25 = 0 \end{matrix}$
$Therefore, the equation of the required line is 2 x - 5 y + 25 = 0$

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