MHB Finding the Equation of a Line Given a Point and Slope

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To find the equation of a line that passes through the point (6, 2) with the same slope as the line represented by the equation 3x + 4y = 12, first solve for y to determine the slope. The slope from the equation is -3/4. Using the point-slope formula, substitute the slope and the point (6, 2) into the equation. This results in the equation y = (-3/4)x + 13/2. The final equation accurately represents the desired line.
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Find an equation of the line that passes through (6, 2) and has the same slope as the line 3x + 4y = 12.

1. Solve the given equation for y. The coefficient of x is the slope.

Yes?

2. I then plug the slope and given point into the point-slope formula and solve for y.

True?
 
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RTCNTC said:
Find an equation of the line that passes through (6, 2) and has the same slope as the line 3x + 4y = 12.

1. Solve the given equation for y. The coefficient of x is the slope.

Yes?

Yes.

RTCNTC said:
2. I then plug the slope and given point into the point-slope formula and solve for y.

True?

That's one way to do it, so yes, that's true.
 
(6, 2) and 3x + 4y = 12.

3x + 4y = 12

4y = -3x + 12

y = (-3/4)x + 12/4

y = (-3/4)x + 3

The slope is (-3/4).

y - 2 = (-3/4)(x - 6)

y - 2 = (-3/4)x + (18/4)

y = (-3/4)x + (18/4) + 2

y = (-3/4)x + (13/2)

Correct?
 
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