Equation of a Line 8.24.17

Equation of a Line Slope formula based on coordinates: (Slope is represented by "m") Points on Lines: If a point lies on a line, the coordinates of the point make the equation true. • Does (4,7) line on the line y = 3x - 5? Yes. 7 = 3(4) - 5 7 = 12 - 5 7 = 7 True.

Different Ways to Write Equations of Lines Slope-Intercept Form:   y = mx + b   (m = slope; b = y-intercept) Use when you know the slope and the y-intercept (where the line crosses the y-axis), or are asked to find the slope and/or y-intercept. Be sure your equation starts with "y =" to use this form. You will need to rewrite the equation if it does not start in this manner.

Slope intercept Find the slope and y-intercept of the equation 4x + 2y = 6. Solution: Rewrite the equation to be "y =": y = -2x + 3 Match your new equation to the form y = mx + b Slope (m) is -2 and y-intercept (b) is +3 Find the equation of a line whose slope is 5 and y-intercept is (0,-6). Solution: The given information tells us that m = 5 and b = -6 Place these values in the form y = mx + b Equation: y = 5x + (-6) or y = 5x - 6

Point Slope Form Point Slope Form:   y - y1= m (x - x1)  m = slope; b = y-intercept;  (x1,y1) = any point on the line • Use when you know a point on the line and the slope (or can determine the slope). • Be sure to subtract the coordinates of your point on the line from y and from x.

Point slope Find the equation of a line with a slope of -1 passing through (-4,6). Solution: The given information tells us that m = -1 and (x1,y1) = (-4,6) Substitute into the form y - y1 = m(x - x1):      y - 6 = -1(x - (-4)) Simplify:   y - 6 = -1(x + 4)   or   y - 6 = -x - 4   or   y = -x + 2   or   x + y = 2 (Your problem may specify what the equation should look like when you simplify.)

Point slope Find the equation of a line passing through (4,-8) and (-2,6). Solution: Find the slope first: Use either point: we will use (4,-8) Substitute into the form y - y1 = m(x - x1): Simplify: or or 3y = -x + 4   or   x + 3y = 4