Understanding the Point-Slope Form | A Math Tutorial on Representing Straight Lines

Point-Slope Form

The point-slope form is one of the forms used to represent the equation of a straight line in mathematics

The point-slope form is one of the forms used to represent the equation of a straight line in mathematics. It describes a line using a specific point on the line and the slope of the line.

The general equation for the point-slope form is:

y – y1 = m(x – x1)

Where:
– (x1, y1) represents the coordinates of a given point on the line.
– m represents the slope of the line.

To use the point-slope form, you need to know the values of both the point on the line and the slope. With this information, you can substitute the values into the equation and simplify to obtain the equation of the line.

For example, let’s say we want to find the equation of a line that passes through the point (2, 4) with a slope of 3. Using the point-slope form, we have:

y – 4 = 3(x – 2)

Expanding this equation gives us:

y – 4 = 3x – 6

We can then rearrange this equation to isolate y:

y = 3x – 6 + 4

Simplifying further:

y = 3x – 2

So, the equation of the line that passes through the point (2, 4) with a slope of 3 is y = 3x – 2.

The point-slope form is particularly useful when you have a specific point and the slope of a line, as it allows you to easily write the equation of the line without needing to calculate intercepts or other additional information.

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