Slope

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Slope Between Two Points

Given two points and , the slope between these two points is . That is, the slope between two points is the difference between the y-coordinates of the points, divided by the difference between the x-coordinates of the points. For example, the slope between the two points (1, 3) and (5, 6) is . The slope between (-1, -1) and (15, -21) is .

Point-Slope Form

The equation for a line with a slope of that goes through some point , in point-slope form, is . For example, the equation of a line with a slope of 3 that goes through the point (1, 4) is . The equation of a line with a slope of that goes through point (-7, -7) is .

Slope-Intercept Form

Another form of an equation of a line is slope-intercept form. The equation of a line with a y-intercept of b (that is, a line that intersects the y-axis at the point (0, b)) and a slope of m is . For example, the equation of a line with a y-intercept of 5 and slope of 6 is . Note that this equation is equivalent to point-slope form. A line with a y-intercept of 5 goes through the point (0, 5), so the point-slope form of this same line is . By adding 5 to each side of the equation, we get the slope-intercept form of the line.

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