Question

Find the equation of the line that passes through (1,3) and is perpendicular to y=2x+3. Leave your answer in the form ax+by=c Where a, b and c are integers.

Answer 1

2y+x=7

Explanation:

The equation of a line is in the form:

`y = mx + c`

where m is the gradient and c is the y-intercept.

In the equation y=2x+3 the gradient is 2, so to find the perpendicular gradient, it is the negative reciprocal, or in other words, flip the number upside down and make it negative:

`2 = (2)/(1)`

`(2)/(1) \: flipped \: upside \: down = (1)/(2)`

`make \: (1)/(2) \: negative = - (1)/(2)`

So the gradient for the point (1, 3) is -1/2

Using y=mx+c to find c (the y-intercept) where y=1, m=-1/2, x=1, substitute these values in:

`y = mx + c`

`3 = - (1)/(2) (1) + c`

`3 = - (1)/(2) + c`

`3 + (1)/(2) = c`

`c = (7)/(2)`

So the equation is:

`y = - (1)/(2) x + (7)/(2)`

We need to write this in the form ax+by=c, so multiply everything by 2 to get rid of the fractions on the right:

`2y = - x + 7`

Bring x to the left side by adding it:

`2y + x = 7`

This is now in the form ax+by=c