Answer :

theleangreenbean

Key Ideas

  • Finding the equation of a line
  • Slope-intercept form

Answering the Question

There are a couple ways we can get the equation of a line, depending on what we're given.

The Equation Form

Most linear equations are organized in slope-intercept form:

[tex]y=mx+b[/tex]

  • m = slope
  • b = y-intercept

Slope

The slope of a line can be calculated algebraically when we know two points that fall on the line:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

  • [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] are the two points

Y-intercept

The y-intercept is the value of y when the line crosses the y-axis, or when x = 0. When given a graph, you can sometimes read the y-intercept directly from the graph.

For instance, if the line passes through the point (0,5), then the y-intercept is 5.

You can also find the y-intercept algebraically if you know the slope and one point that falls on the line. You plug in that point as (x,y) and isolate b.

Summary

For most cases, you can use the following method to find the equation of a line:

  1. Find the slope of the line (using the slope equation) and plug it into y=mx+b
  2. Find the y-intercept of the line algebraically and plug it into y=mx+b

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