Question

Find the equation of a line whose $x$ intercept is 5 and passing through the point (4, -7).

• A. $y=7x-42$
• B. $y=5x-35$
• C. $y=5x-28$
• D. $y=7x-35$

Answer 1

The correct option is D

$y=7x-35$

Given : line passess through point (4,-7)
$x$ intercept = 5
$\therefore$ its coordinates are (x, y) = (5,0)
$\therefore Slope=\frac{y_2-y_1}{x_2-x_1}=\frac{0+7}{5-4}=\frac{7}{1}$
$\therefore m=7$

Equation of straight line is:
$y-y_1=m(x-x_1)$
[Point - slope form]
$Here,m=7,x_1=4,y_1=-7$
$\Rightarrow y-0=7(x-5)$
$\Rightarrow y=7x-35$