Question

If the x-intercept of the line is 3 units and y-intercept is 2 times x-intercept, then find the equation of the line

Answer 1

Answer:

x+2y=12

Step-by-step explanation:

the line passing through (0,6) and (3,0)

from the given data

now

(x-0)=(-6/3)(y-6)

x=-2(y-6)

x+2y=12

Answer 2

We need to recall the following definition of the point-slope form of a linear equation.

If a straight line with a slope $m$ passes through a point $(x_1,y_1)$ , then the equation of the line is $y-y_1=m(x-x_1)$.

This problem is about the point-slope form of a linear equation.

Given:

$x$ - intercept of the line is $(3,0)$

$y$ - intercept is $2$ times $x$ - intercept. i.e., $(0,6)$

The line passes through the points $(0,6)$ and $(3,0)$.

So, the slope of the line is,

$m=\frac{0-6}{3-0}$

$m=-2$

From the point-slope form of a linear equation, we get

$y-0=-2(x-3)$

$y=-2x+6$

$2x+y-6=0$

Hence, the equation of the line is $2x+y-6=0$.