What is the equation of a line passing through (6, -3) with a y-intercept of 8?

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Discussion Overview

The discussion revolves around finding the equation of a line that passes through the point (6, -3) and has a y-intercept of 8. Participants explore the steps involved in deriving the equation, focusing on the slope and the appropriate form of the equation.

Discussion Character

  • Technical explanation
  • Mathematical reasoning

Main Points Raised

  • One participant outlines a method involving finding the slope, using the point-slope formula, and solving for y, while seeking confirmation of this approach.
  • Another participant presents a formula for a line passing through a point with a given y-intercept, expressed in slope-intercept form.
  • Several participants question the correctness of their own or others' information regarding the steps to derive the equation.
  • A participant suggests that simply solving for y is insufficient unless the equation is arranged in slope-intercept form, proposing an alternative arrangement of the equation.
  • One participant clarifies that by "solving for y," they specifically mean to express it in slope-intercept form, y = mx + b.

Areas of Agreement / Disagreement

Participants express uncertainty about the correctness of their approaches and the steps involved, indicating that multiple interpretations of the process exist without a clear consensus on the best method.

Contextual Notes

There is a lack of clarity regarding the definitions and assumptions related to the slope and the arrangement of the equation, as well as the specific requirements for expressing the final answer.

mathdad
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Find an equation of the line passing through (6, -3) and has y-intercept 8. Express final answer in the form y = mx + b.

If it has y-intercept 8, this means the point (0, 8).

I now have 2 points.

1. Find the slope

2. Use the point-slope formula

3. Solve for y

Correct?
 
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A line passing through the point:

$$\left(x_1,y_1\right)$$

And having the $y$-intercept $b$, expressed in slope intercept form, will be:

$$y=\frac{y_1-b}{x_1}x+b$$
 
Is my information correct?
 
RTCNTC said:
Is my information correct?

Essentially, although I would change step 3 to read "Arrange in slope-intercept form." It's not enough to just solve for y, because we could have solved for y but not used the slope-intercept form, such as:

$$y=m(x-a)+b$$

We would want to arrange this as:

$$y=mx+(b-ma)$$
 
By solving for y I meant slope-intercept form y = mx + b.
 

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