Help+for+Equations+of+Line

Model Problem 1 ) 1) What is the equation of a line with a slope of 3 that goes through the point (2,8) ? Step 1) substitute slope into equation y =mx + b y = 3x + b

Step 2) substitute (2,8) into equation 8 = 3(2) +b

Step 3) solve for b 8 = 6 + b 2 = b

Step 4) Insert B into equation y = 3x + 2

Model problem 2 ) What is an equation for the line that passes through the coordinates (4,5) and (8, 3)? 1) Calculate Slope (5 - 3)/(4 - 8) = 2/-4 = -1/2

2) Plug it into the slope intercept formula: Y = (-1/2)X + b

3) Plug the x and y given in the question into the slope intercept formula 5 = (-1/2) (4) + b

4) Solve for b 5 = (-1/2) (4) + b 5 = -2 + b +2 +2 7 = b

5) Rewrite equation in slope intercept form Y = (-1/2)X + 7

Model Problem 3) Write the equation of a line that is parallel to y = 2x + 3 and passes through the points (6,2).

Step 1) plug slope the slope intercept formula: y = mx + b y = 2x + b

2) Plug the x and y given in the question into the slope intercept formula 2 = 2(6) + b

3) Solve for b 2 = 12 + b -12 -12 -10 = b

4) Rewrite equation with only slope and y-intercept y = 2x – 10

Model Problem 4) Write the equation of a line that is perpendicular to Y = (1/2)X – 6 and passes through the point (6,4) ?

Step 1) find the negative reciprocal of the slope Slope = 1/2 Negative reciprocal = -2

2) Plug the x and y given in the question into slope intercept formula 4 = -2(6) + b

3) Solve for b 4 = -12 +b +12 +12 16 = b

4) Rewrite equation in slope intercept form y = -2x + 16

Model Problem 5) Write the equation of the perpendicular bisector that goes through the line segment with end points of A (2,1) and B (6, -3)

Step 1) Find the slope of the line segment using the points given (1- -3) / (2 - 6) = (1+3) / -4 = **-1**

Step 2) Find the slope of a line that is perpendicular to the original line segment, -1. -(-1/1) = **1**

Step 3) Find the midpoint of the original two points [(2+6) / 2, (1+ -3) / 2] = [8/2 , (1-3)/2] = [4 , -2/2] = **[4 , -1]**

Step 4) Use the midpoint and new slope to solve for the y-intercept y = mx + b Y = 1X + b -1 = 1(4) + b -1 = 4 + b -4 -4 -5 = b

Step 5) Write the equation using new slope and y-intercept **Y = X - 5**