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The equation of the line that goes through the point .............................................................

The equation of the line that goes through the point .............................................................-example-1
User Daniel Weiner
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2 Answers

22 votes
22 votes

Answer:

y = 3/4 x -3

Step-by-step explanation:

4 x + 3y = 3

3y = -4x + 3

y = -4/3x + 1

~~~~~~~~~~~~~~~~~~~~~~~

y = 3/4 x + b

3 = 3/4(5) + b

12 = 15 + b

B = -3

User Cihan Keser
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27 votes
27 votes

Answers:

  • m = 3/4
  • b = -3/4

Note: 3/4 = 0.75

====================================================

Step-by-step explanation:

The first thing we need to do is solve that given equation for y

4x+3y = 3

3y = 3-4x

3y = -4x+3

y = (-4x+3)/3

y = (-4x)/3 + 3/3

y = (-4/3)x + 1

This last equation is in slope intercept form, y = mx+b, where,

  • m = -4/3 = slope
  • b = 1 = y intercept

These m and b values are not the final answer unfortunately, as we have yet to determine anything about the perpendicular line. However, it helps us build toward the answer.

We'll focus on the slope.

Apply the negative reciprocal to -4/3 to get 3/4. We flip the fraction and the sign from negative to positive.

This means the perpendicular slope is 3/4 and this value goes in the first box.

-----------------------------

From here, we'll use the fact that the perpendicular line goes through the point (x,y) = (5,3)

i.e. we have x = 5 and y = 3 pair up together.

Use that perpendicular slope we found earlier to say,

y = mx+b

3 = (3/4)*5 + b

3 = 15/4 + b

3 - 15/4 = b

12/4 - 15/4 = b

(12-15)/4 = b

-3/4 = b

b = -3/4 is the y intercept of the perpendicular line

User Mutix
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2.7k points