Math 1123 || ACE

finding the equation of a line by using the point-slope equation

(y - y1) = m(x - x1)

finding the equation of a line by using the two-point equation

(y - y1) = y2 - y1 / x2 - x1 (x - x1)

dependent (equivalent) linear equations

- graphs of the solution sets of two linear equations will form lines that may have all points in common - lines coincide - the slopes and y-intercepts of these equations are the same

consistent linear equations

- graphs of the solution sets of two linear equations will form lines that may have exactly one point in common - lines intersect - slopes are different (if their slopes are negative reciprocals whose product is -1, then the lines are perpendicular)

inconsistent linear equations

- graphs of the solution sets of two linear equations will form lines that may have no points in common - the lines are parallel - the slopes are the same, but the y-intercepts are different

solving simultaneous equations by using the linear combinations method

1. add the left side of both equations 2. add the right side of both equations 3. equate the resulting two sums

solving simultaneous equations by using the substitution method

finding x or y in one equation, using that information in the other equation, then finding the other variable in the original equation

finding the slope of the line

m = y2 - y1 / x2 - x1

finding the slope and y-intercept of a line

y = mx + b