How to Write an Equation in Point-Slope Form for the Line Through the Point (8, 3) with Given Slope?

To write the equation of a line in point-slope form, we use the formula:

y – y₁ = m(x – x₁)

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

In this case, we are given the point (8, 3) and the slope m = 8.

Plugging these values into the point-slope formula, we get:

y – 3 = 8(x – 8)

This equation represents the line that goes through the point (8, 3) with a slope of 8. To further understand:

• The left side (y – 3) adjusts the y-coordinate at the point (8, 3), indicating that the line will go through this specific point.
• The right side (8(x – 8)) shows how steep the line is; for every 1 unit you move to the right along the x-axis, you will move up 8 units on the y-axis.

This simple form is very useful for graphing the line or finding additional points on it.