Forms of Linear Equations: Point-Slopey-y 1 = m(x-x 1 ) Slope Intercept y= mx+b Standard FormAx+By=C Review: Points are: (x 1,y 1 ) (x 2,y 2 ) m = Slope b = y-intercept Working with Point-Slope Form: Through point (x1, y1) with slope m: y-y 1 =m(x-x 1 ). Example: You are given a line that goes through the points (1,2) and (3,4). Find the equation of the line in point-slope form. Step One: Find the slope of the two points. Subtracting the x 1 from the x 2 and y 1 from the y = = Step Two: Plug found slope and one set of points, either (1,2) or (3,4), into point-slope form equation. Using (1,2): y-2=1(x-1) Using (3,4): y-4=1(x-3) Answers: y-2=1(x-1) or y-4=1(x-3) Working with Slope Intercept Form: y=mx+b, consists of the y-intercept and slope. Example: You are given a line that goes through the points (5,6) and (11,9). Find the equation of the line in slope intercept form. Step One: Find the slope of the two points. Subtracting the x 1 from the x 2 and y 1 from the y = = Step Two: Find the b of the equation by plugging in the found slope and one set of points, either (5,6) or (11,9) into the slope intercept equation. Using (5,6): 6=(5)+b 6=2.5+b3.5=b Using (11,9): 9=(11)+b9=5.5+b3.5=b Step Three: Plug found slope and b into slope intercept equation. y=x+3.5 Answer: y=x+3.5 Converting Point-Slope to Slope Intercept Form: y-y 1 =m(x-x 1 ) to y=mx+b Example: You are given the equation, y-2=1(x-1), in point-slope form. Convert it to slope intercept form. Step One: Distribute the y 2, or in this equation the 2, onto the opposite side of the equation. y=1(x-1)+2 Step Two: Distribute the slope, or in this equation the 1, through the parenthesis (x-1). y=x-1+2 Step Three: Add the distributed number and y 2, the -1 and 2 in this equation. y=x+1 Answer: y=x+1 Working with Standard Form: Ax+By=C, where A, B, and C are real numbers and A and B are not both zero. Example: You are given the equation, 4x+8y=16, in standard form. Solve for x and y. Step One: Solve for x first, plug 0 in for y. 4x+0=164x=16x=4 Step Two: Solve for y second, plug 0 in for x. 0+8y=168y=16y=2 Answer: x=4 and y=2 Graphing an Equation Using Intercepts: Example: What are the intercepts of 7x+2y=14? Graph the equation. Step One: Solve for x first, plug 0 in for y. 7x+0=147x=14x=2 Step Two: Solve for y second, plug 0 in for x. 0+2y=142y=14y=7 Step Three: Plot the points (2,0) and (0,7). Answers: x=2, y=7 and Types of Linear Equations: Parallel Lines Are equal. They have the same slope but different y-intercepts and they will never cross. m 1 =m 2 Example: 1=1 Perpendicular Lines Are negative reciprocals of each other. Have opposite slopes and cross, making a 90 angle. m 1 =- 1 /m 2 Example: 2=-1/2 Finding Perpendicular Lines: Example: You are given the equation, y=2x+6. Find the equation of the line that is perpendicular to it and goes through the points (3,4). Step One: Find the opposite slope. 2=-1/2 Step Two: Plug opposite found slope -1/2 and the points (3,4) in a point-slope form equation. y-4=-1/2(x-3) Step Three: Convert equation, y-4=-1/2(x-3), to slope intercept form. y=-1/2(x-3)+4y=-1/2x y=-1/2x+5.5 Answer: The line perpendicular to y=2x+6 is y=-1/2x+5.5