First slide

Equation of line in Straight lines

Question

Equation of line passing through the point $(5, 7)$ and slope is equal to slope of the line joining through the points $(3, 7)$ and $(5, 3)$ is $a x + b y + c = 0$ then $a + b =$

Moderate

A

1
B

2
C

3
D

4

Solution

$Slope of the line joining the points (3, 7) and (5, 3) is m = \frac{3 - 7}{5 - 3} = - 2$
$Equation of the line having the slope m and passing through the point (x_{1}, y_{1}) is$
$y - y_{1} = m (x - x_{1})$
$Hence the equation of the line having slope m = - 2 and passing through the point (5, 7) is$
$\begin{matrix} y - 7 = - 2 (x - 5) \\ y - 7 = - 2 x + 10 \\ 2 x + y - 17 = 0 \end{matrix}$
$Compare the above equation with a x + b y + c = 0$
$a = 2, b = 1$
$Therefore, a + b = 3$

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