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slope vocabulary & steps to solve certain situations

slope

the steepness of a line on a graph, equal to its vertical change divided by its horizontal change; rise over run; rate of change

slope formula

m=y₂-y₁/x₂-x₁

slope-intercept form

y=mx+b, where m is the slope and b is the y-intercept of the line.

direct variation

an equation of the form y = kx, where k is not equal to 0; "y varies directly with x"; k = y/x

constant of variation

the slope, or rate of change, in the equation y=kx, represented by k

Point-Slope Form

y - y1 = m(x - x1); use when given a point & a slope

Write an equation of a line given two points (x1, y1) & (x2, y2)

Step 1: Find slope
Step 2: Use one point and the slope and plug in point-slope form
Step 3: Solve for y to get it in slope-intercept form

Standard Form

Ax + By=C, where A, B, and C are not decimals or fractions, where A and B are not both zero, and where A is not a negative

Find the slope & y-intercept when given Standard Form

m = -A/B; b = C/B

Parallel lines

Have the same slope, different y-intercepts.

Perpendicular lines

Have opposite & reciprocal slopes

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