Graphing and Writing Equations of Lines (2-4) Objective: Graph linear equations and write the equations of lines in slope-intercept and point-slope form.

Forms of Linear Equations There are three main forms for the equation of a line Slope-Intercept Form y = mx + b m = slope b = y-intercept Standard Form Ax + By = C A, B and C integers A > 0, A and B not both 0 Point-Slope Form y - y1 = m(x – x1) (x1, y1) is any point on the line

Graphing Lines From slope intercept form Determine the y-intercept and plot it on the graph FIRST Determine the slope and use it to find one or more additional points Connect the points. Don’t forget to put arrows on the ends.

Graphing Lines Example: Graph Graph the y-intercept of -5 From the y-intercept, use the slope to rise 2 and run 3. This will give you a second point. Repeat. Use a ruler to connect the points and create a line. . . .

Graphing Lines From Standard Form Method 1: convert to slope-intercept form Method 2: find x- and y-intercepts

Graphing Lines Graph 3x + 4y = 24 x – intercept y-intercept . .0.

Graphing Lines From point-slope form Determine the point (x1, y1) Graph the point Use the slope to find additional points Draw the line

Graphing Lines Graph y – 5 = -2(x + 1) Rewrite as y – 5 = -2(x - -1) The point is (-1, 5) Graph the point The slope is -2/1, so rise -2 and run 1 .

Writing Equations of Lines You must be given two pieces of information to write the equation of a line. This information can be Slope and y-intercept Slope and one point Two points If you are given the graph of a line, you can get that information from the graph.

Writing Equations of Lines b = -1 y = mx + b b = -1 -1 y = ___x + ___ rise = -2 run = 3

Writing Equations of Lines Write the equation of a line with slope -3 and one point at (-5, 2) When given the slope and one point, it is easiest to use the point-slope form y – y1 = m(x – x1) y – 2 = -3(x - -5) y – 2 = -3(x + 5) covert to slope-intercept y – 2 = -3x – 15 y = -3x - 13

Writing Equations of Lines When given two points you need to: Use the slope formula to determine the slope Use the calculated slope and one of the two points to determine the equation of the line

Writing Equations of Lines Write the equation of the line passing through (-3, 5) and (6, -2). Find the slope Use the slope and one of the two points to write the equation y – y1 = m(x – x1)

Parallel and Perpendicular Lines Parallel lines have the SAME slope Perpendicular lines have slopes that are OPPOSITE RECIPROCALS

Parallel and Perpendicular Lines Find the equation of the line parallel to 3x + 5y = 7 and passing through (10, -2) Find the slope of the original line: From standard form, slope is –A/B The slope of the line above is -3/5, so the slope of the parallel line is also -3/5 Use the slope and the point to write the equation

Parallel and Perpendicular Lines Find the equation of the line perpendicular to 8x – 2y = 9 and with y-intercept -4 Find the slope of the line: -A/B = -8/-2 = 4 The slope of the line perpendicular to the given line would be Use the slope and the y-intercept to write the equation of the line