Question

Find the equation of the straight line passing through the point (-4,5) and perpendicular to the line y=2x+7.Suppose the equation is y=cx+d.Find c,d.

Answer 1

The equation of the line is:

`y = -(1)/(2)x + 3`

Explanation:

Equation of a line:

The equation of a line has the following format:

`y = mx + b`

In which m is the slope and b is the y-intercept.

Perpendicular lines:

If two lines are perpendicular, this means that the multiplication of their slopes is -1.

Perpendicular to y=2x+7

This means that:

`2m = -1`

`m = -(1)/(2)`

So

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

Passing through the point (-4,5)

This means that when
`x = -4, y = 5`. We use this to find b.

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

`5 = -(1)/(2)(-4) + b`

`2 + b = 5`

`b = 3`

The equation of the line is:

`y = -(1)/(2)x + 3`