Finding the Equation of a Line with Point-Slope Formula

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In summary, the equation of the line with slope m = a/b and passing through the point (a, b) can be found using the point-slope formula: y - b = (a/b)(x - a). Simplifying this equation gives the final equation of y = (a/b)x + (b^2 - a^2)/b.
  • #1
mathdad
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Given m = a/b and the point (a, b), find the equation of the line.

I got to use the point-slope formula.

y - y_1 = m(x - x_1)

y - b = (a/b)(x - a)

y - b = (a/b)x - (a^2)/b

y = (a/b)x - (a^2)/b + b

y = (a/b)x + (b^2 - a^2)/b

Is this correct?
 
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  • #2
RTCNTC said:
Given m = a/b and the point (a, b), find the equation of the line.

I got to use the point-slope formula.

y - y_1 = m(x - x_1)

y - b = (a/b)(x - a)

y - b = (a/b)x - (a^2)/b

y = (a/b)x - (a^2)/b + b

y = (a/b)x + (b^2 - a^2)/b

Is this correct?

That is correct.
 
  • #3
Very good.
 

FAQ: Finding the Equation of a Line with Point-Slope Formula

What is the equation of a line?

The equation of a line is a mathematical representation of a straight line, 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 know the slope and the y-intercept. You can find the slope by using the formula (y2 - y1)/(x2 - x1), where (x1, y1) and (x2, y2) are any two points on the line. Once you have the slope, you can plug it in along with the coordinates of any point on the line into the equation y = mx + b to find the y-intercept.

What is the slope-intercept form of the equation of a line?

The slope-intercept form of the equation of a line is y = mx + b, where m is the slope and b is the y-intercept. This form is useful for graphing a line and quickly identifying the slope and y-intercept.

Can the equation of a line have a negative slope?

Yes, the slope of a line can be positive, negative, or zero, depending on the steepness and direction of the line. A negative slope means that the line is decreasing as you move from left to right on the graph.

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

The y-intercept represents the point where the line intersects the y-axis on a graph. It is also the value of y when x is equal to 0. This point is important because it helps us to identify the starting point or initial value of the line.

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