Understanding the Point Slope Form: A Simple Guide to Writing Equations of Straight Lines

Point Slope Form

The point slope form is a way to write the equation of a straight line

The point slope form is a way to write the equation of a straight line. It is given by:

y – y1 = m(x – x1),

where (x1, y1) is a point on the line and m is the slope of the line.

To understand this form, let’s break it down:

– (x1, y1) represents any point on the line. It could be the coordinates of a given point, or you can choose any point on the line that you want to use.

– The slope, denoted by m, is a measure of how steep the line is. It determines the rate at which the y-coordinate changes relative to the x-coordinate. For example, if the slope is 2, then for every 1 unit increase in x, the y-coordinate will increase by 2 units.

The point slope form is useful for finding the equation of a line when you are given a point on the line and its slope. Here’s how you can use it:

1. Start with a given point (x1, y1) on the line and its slope, m.
2. Substitute the values of x1, y1, and m into the point slope form equation.
3. Simplify the equation.

For example, let’s say we are given a line with a slope of 2 that passes through the point (3, 4). We can use the point slope form to find the equation of the line.

Using the point slope form:

y – 4 = 2(x – 3).

Now we can simplify the equation:

y – 4 = 2x – 6.

To find the slope-intercept form (y = mx + b) from the point slope form, we can rearrange the equation:

y = 2x – 6 + 4.

Simplifying further:

y = 2x – 2.

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

In summary, the point slope form is a useful tool for writing the equation of a line when given a point on the line and its slope. It provides a clear and concise representation of a line’s equation.

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