Question

The equation for line f can be written as y=9/5x–2. Perpendicular to line f is line g, which passes through the point (5,–3). What is the equation of line g?

Write the equation in slope-intercept form. Write the numbers in the equation as simplified proper fractions, improper fractions, or integers.

Answer 1

y = -5/9x -2/9

Explanation:

Answer 2

Perpendicular Lines

When a line is perpendicular, it means that their slope is the negative reciprocal of the reference line.

Examples of negative reciprocals:

1/3 and -3

-4/7 and 7/4

Solving the Question

We're given:

• 
  `y=(9)/(5)x-2`
• Passes through (5,–3)

Slope intercept form:
`y=mx+b`

• m = slope
• b = y-intercept

Finding the slope

We know that the slope of the line will be the negative reciprocal of
`(9)/(5)`:

`-(5)/(9)`

⇒ Plug this into y=mx+b:

`y=-(5)/(9)x+b`

Finding the y-intercept

To find the y-intercept, plug in the given point and solve for b:

`-3=-(5)/(9)*5+b\\\\-3=-(25)/(9)+b\\\\b=-(2)/(9)`

⇒ Plug this into our equation:

`y=-(5)/(9)x-(2)/(9)`

Answer

`y=-(5)/(9)x-(2)/(9)`