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Straight-line equations are those that are first degree in both x and y.

Slope: the measure of “steepness” of a line. Two points on the line are needed to determine the slope.

where (x1, y1) and (x2, y2) are the coordinates of any two points on the line

Line Equations:

Point-Slope Form: y - y1 = m(x - x1) where (x1, y1) is the point and m is the slope Need a point and the slope to use this form
Slope-Intercept Form: y = mx + b where m is the slope and b is the y-intercept (0,b) Need a slope and a point on the line, OR Need the slope and y-intercept

* Equations must be in the slope-intercept form (solved for y ) in order to easily “see” what the slope and y -intercept are.

Parallel Lines… have the same slopes and different y-intercepts

Perpendicular Lines… have slopes that are negative reciprocals. If the slope of one line is 4 , then the slope of the perpendicular line is .

Graphing Linear Equations:

  • Find the x -intercept by letting y = 0, then find the y -intercept by letting x = 0. Plot these two points, and draw the line that connects the two points.
  • If the equation is given in slope-intercept form: Plot the y -intercept first. From the y -intercept, use the slope information to go up/down, then right, to obtain another point. Connect these two points, and you have graphed the line.

Vertical Lines… are missing the y variable. The slope of a vertical line is undefined. x = 3 is the equation of a vertical line, where the x coordinate is always 3, and the y coordinate can be any value.

Horizontal Lines… are missing the x variable. The slope of a horizontal line is zero. y = 2 is the equation of a horizontal line, where the y coordinate is always 2, and the x coordinate can be any value.

Horizontal and Vertical lines are perpendicular.