Finding the Equation of a Line Given a Point and Slope

  • MHB
  • Thread starter mathdad
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In summary, to find an equation of the line that passes through (6, 2) and has the same slope as the line 3x + 4y = 12, you can solve for y in the given equation and use the slope to plug into the point-slope formula. The resulting equation is y = (-3/4)x + (13/2). This is the correct equation.
  • #1
mathdad
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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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  • #2
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.
 
  • #3
(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?
 

FAQ: Finding the Equation of a Line Given a Point and Slope

What is the equation of a line?

The equation of a line is a mathematical representation of a straight line on a graph. It is typically written in the form y = mx + b, where m is the slope of the line and b is the y-intercept.

How do you find the equation of a line?

To find the equation of a line, you need to have two points on the line. Then, you can use the slope formula (m = (y2 - y1) / (x2 - x1)) to find the slope. Finally, plug the slope and one of the points into the point-slope formula (y - y1 = m(x - x1)) to get the equation of the line.

What is the significance of the slope and y-intercept in the equation of a line?

The slope represents the rate of change of the line. It tells us how much the y-value changes for every one unit increase in the x-value. The y-intercept represents the point where the line crosses the y-axis.

Can the equation of a line have a negative slope?

Yes, the slope of a line can be positive, negative, or zero. A negative slope indicates a downward trend, while a positive slope indicates an upward trend.

What is the difference between the slope-intercept form and the standard form of the equation of a line?

The slope-intercept form (y = mx + b) is easier to use and interpret because the slope and y-intercept are explicitly stated. The standard form (Ax + By = C) is useful for graphing and finding the x and y intercepts, but it is not as intuitive as the slope-intercept form.

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