Point-Slope Form: How To Express The Equation Of A Line?

Point Slope Form

y-y₁=m(x-x₁)

Point-slope form is a way of expressing the equation of a line, which can be written as y – y1 = m(x – x1), where (x1, y1) represents a point on the line, and m represents the slope of the line.

To understand point-slope form, it’s helpful to know what slope is. The slope of a line is the measure of how steeply it rises or falls over a certain distance. It’s given by the formula m = (y2 – y1) / (x2 – x1), where (x1, y1) and (x2, y2) are two points on the line. If we know the slope of a line and a point on the line, we can use point-slope form to find the equation of that line.

Let’s take an example to understand this better. Suppose we have a line that passes through the point (4, 5) and has a slope of 2. We can write the equation of this line in point-slope form as y – 5 = 2(x – 4). Now, let’s simplify this equation to convert it into slope-intercept form y = mx + b, where m is the slope and b is the y-intercept. To do that, we’ll solve for y by distributing the number 2 and adding 5 to both sides, which gives us:

y – 5 = 2(x – 4)
y – 5 = 2x – 8
y = 2x – 8 + 5
y = 2x – 3

So the equation of the line that passes through the point (4, 5) and has a slope of 2 is y = 2x – 3 in slope-intercept form. We can use this form to find the y-coordinate of any point on the line by plugging in the corresponding x-coordinate.

In summary, point-slope form is a useful way to express the equation of a line when we know a point on the line and its slope. It allows us to find the equation of the line quickly and easily, and then convert it into other forms if needed.

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