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Olenka [21]
3 years ago
13

Write the equation in slope-intercept form of the line that passes through

Mathematics
1 answer:
mixer [17]3 years ago
7 0

Answer:

We conclude that the equation in slope-intercept form of the line that passes through  (12,9) and is perpendicular to the graph of y = -3/4x + 1 will be:

  • y=\frac{4}{3}x-7

Step-by-step explanation:

We know the slope-intercept form of the line equation

y = mx+b

where

  • m is the slope
  • b is the y-intercept

Given the line

y = -3/4x + 1

comparing with the slope-intercept form of the line equation

The slope = m = -3/4

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:  

slope = m = -3/4

Thus, the slope of the new perpendicular line = – 1/(-3/4) = 4/3

Using the point-slope form

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 values of the slope = 4/3 and the point (12, 9)

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

y-9=\frac{4}{3}\left(x-12\right)

Add 9 to both sides

y-9+9=\frac{4}{3}\left(x-12\right)+9

y=\frac{4}{3}x-16+9

y=\frac{4}{3}x-7

Therefore, we conclude that the equation in slope-intercept form of the line that passes through  (12,9) and is perpendicular to the graph of y = -3/4x + 1 will be:

  • y=\frac{4}{3}x-7
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It's a similar triangle so the ratios of corresponding sides should be equal which means

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