# Thread: Equation of the line

1. ## Equation of the line

How do you solve this?

The line $\displaystyle y= 4x+8$ meets the y-axis at the point B. Find the equation of the line with gradient 2 that passes through the point B.

Spoiler:
$\displaystyle y=4x+8$
$\displaystyle 4x+8=0$
$\displaystyle 4x=8$
$\displaystyle x=2$

totally confused

2. If x=0, then y=0+8=8.
Therefore (0,8) is the y-axis crossing point.

A line with gradient 2, passing through this point is $\displaystyle y=2x+8$

The gradient is called "m" as it is the multiplier of x
when the linear equation is expressed in the form y=mx+c.

3. Originally Posted by Mist
How do you solve this?

The line $\displaystyle y= 4x+8$ meets the y-axis at the point B. Find the equation of the line with gradient 2 that passes through the point B.

Spoiler:
$\displaystyle y=4x+8$
$\displaystyle 4x+8=0$
$\displaystyle 4x=8$
$\displaystyle x=2$

$\displaystyle y=mx+b$,m is the gradient (slope),b is the y-intercept.
$\displaystyle m=2$ and $\displaystyle B=(0,8)$
$\displaystyle y=2x+8$.