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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.

Sagot :

theleangreenbean

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:

  • [tex]y=\dfrac{9}{5}x-2[/tex]
  • Passes through (5,–3)

Slope intercept form: [tex]y=mx+b[/tex]

  • m = slope
  • b = y-intercept

Finding the slope

We know that the slope of the line will be the negative reciprocal of [tex]\dfrac{9}{5}[/tex]:

[tex]-\dfrac{5}{9}[/tex]

⇒ Plug this into y=mx+b:

[tex]y=-\dfrac{5}{9}x+b[/tex]

Finding the y-intercept

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

[tex]-3=-\dfrac{5}{9}*5+b\\\\-3=-\dfrac{25}{9}+b\\\\b=-\dfrac{2}{9}[/tex]

⇒ Plug this into our equation:

[tex]y=-\dfrac{5}{9}x-\dfrac{2}{9}[/tex]

Answer

[tex]y=-\dfrac{5}{9}x-\dfrac{2}{9}[/tex]

Answer:

y = -5/9x -2/9

Step-by-step explanation:

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