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 graph a line from a point in the slope and then list some other

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 represents its steepness and is defined as the ratio of the vertical change (rise) to the horizontal change (run) between any two distinct points on the line. In this problem, a slope of -1 means that for every unit increase in the x-coordinate, the y-coordinate decreases by one unit, which is the key relationship used to determine other points on the line.

Point-Slope Form

The point-slope form is an equation of a line that is particularly useful when you know one point on the line and the slope. It is expressed as y - y? = m(x - x?), where (x?, y?) is a point on the line and m is the slope. This form allows you to easily calculate additional points on the line by substituting different x values and solving for y.

Finding Additional Points

Once you have the slope and a known point, you can determine other points on the line by applying the slope repeatedly. By increasing or decreasing the x-value and adjusting the y-value according to the slope, you derive new coordinates that lie on the line. This method is essential for understanding how the linear relationship extends across the coordinate plane.

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