Use the point on the line and the slope m of the line to find three additional points through wh

step 1 In this problem, we are going to use a point in the slope to sketch a line and find some additio

Use the point on the line and the slope m of the line to...

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Key Concepts

Slope

The slope of a line indicates the rate at which the y-coordinate changes with respect to the x-coordinate. It is calculated as the ratio of the vertical change (rise) to the horizontal change (run) between any two points on the line. A slope of 1 means that for every one unit increase in x, there is an equivalent one unit increase in y.

Point on a Line

A point on a line is a coordinate pair that satisfies the equation of the line. This known point can be used as a reference when writing the equation of the line or when finding additional points that lie on the same line.

Point-Slope Form

The point-slope form is a method for writing the equation of a line when a point on the line and the slope are known. It is expressed as y - y? = m(x - x?), where m is the slope and (x?, y?) is the given point, and it simplifies the process of finding other points on the line.

Finding Additional Points Using the Slope

Once the slope and a point on the line are known, additional points can be found by applying the slope as a step. By increasing or decreasing the x-coordinate by a specific value and adjusting the y-coordinate by m times that change, one can generate new points that lie on the line.

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