What Is Given

What is given?

Two points The graph One point One point and and slope another equation

Find two points Find one point If the line is If the line is and the slope parallel, use perpendicular, the same slope. use the negative reciprocal slope.

Find the slope y- y m = 2 1 x- x 2 1 Use point-slope form

y  y1 = m(x – x1)

Special case: If m Write in slope-intercept form Special case: If is undefined, the y = mx + b the equation is a equation is x = x1 direct variation, one point is (0, 0).

Write in standard form (if needed) ax + by = c How do you write the equation of a line? Given Example Your Turn *****Slope and Y-intercept***** ***Slope = ¾, y-intercept = -2*** ***Slope = - ½ , y-intercept = 5*** Use the slope-intercept form of the equation: y = mx + b 3 y= x-2 Substitute for m and b. 4 *****Slope and a Point***** ***Slope = -3, Point = (-2, 4)*** ***Slope = 4, Point = (-6, -4)***

Use the point-slope form of the equation: y – y1 = m(x – x1)

y – y1 = m(x – x1) y – 4 = -3(x – -2)

Substitute for m, x1 and y1. Solve for y. *****Two Points***** *** Points are (-3, 3) and (2, -7)*** *** Points are (-11, -2) and (1, -8)*** Use the slope formula and the coordinates of the two points to find the slope.

m = rise = y2 – y1

run x2 - x1 Use this slope and one of the given points to write the equation of the line following the ****Slope and a Point***** method above. ***Point and the Equation of a Parallel Line*** *** Point is (-6, -3) and parallel line’s *** Point is (-2, 5) and parallel line’s Solve the equation of the parallel line for y and find equation is y -2x = 6*** equation is y=3x+5*** its slope. Use this slope and the given point to write the equation of the line following the *****Slope and a Point***** method above.

**Point and the Equation of a Perpendicular Line** *** Point is (6, -4) and perpendicular *** Point is (6, -4) and perpendicular Solve the equation of the perpendicular line for y line’s equation is 4x - 2y = -6*** line’s equation is 3x + 9y = -8*** and find its slope. Use the opposite reciprocal of that slope and the given point to write the equation of the line following the *****Slope and a Point***** method above.