Question

Which is an equation of the line passing through (-2, 3) and perpendicular to the line 5x - y = 12?

Answer 1

An equation of the line passing through (-2, 3) and perpendicular to the line 5x - y = 12 will be:

• 
  `y=-(1)/(5)x+(13)/(5)`

Explanation:

Given the equation

`5x - y = 12`

converting the line into the slope-intercept form y = mx+b, where m is the slope

`-y = 12-5x`

`y = 5x-12`

The slope of the line = m = 5

We know that a line perpendicular to another line contains a slope that is the negative reciprocal of the slope of the other line, such as:

Therefore, the slope of new line = – 1/m = -1/5 = -1/5

Using the point-slope form of the line equation

`y-y_1=m\left(x-x_1\right)`

where m is the slope of the line and (x₁, y₁) is the point

substituting the slope of new line = -1/5 and (-2, 3)

`y-y_1=m\left(x-x_1\right)`

`y-3=-(1)/(5)\left(x-\left(-2\right)\right)`

`y-3=-(1)/(5)\left(x+2\right)`

Add 3 to both sides

`y-3+3=-(1)/(5)\left(x+2\right)+3`

`y=-(1)/(5)x+(13)/(5)`

Therefore, an equation of the line passing through (-2, 3) and perpendicular to the line 5x - y = 12 will be:

• 
  `y=-(1)/(5)x+(13)/(5)`