5.2 Equations of Lines Given the Slope and a Point

43210 In addition to level 3.0 and above and beyond what was taught in class, the student may: · Make connection with other concepts in math · Make connection with other content areas. The student will understand that linear relationships can be described using multiple representations. - Represent and solve equations and inequalities graphically. - Write equations in slope-intercept form, point-slope form, and standard form. - Graph linear equations and inequalities in two variables. - Find x- and y- intercepts. The student will be able to: - Calculate slope. - Determine if a point is a solution to an equation. - Graph an equation using a table and slope- intercept form. With help from the teacher, the student has partial success with calculating slope, writing an equation in slope- intercept form, and graphing an equation. Even with help, the student has no success understanding the concept of a linear relationships. Learning Goal #1 for Focus 4 (HS.A-CED.A.2, HS.REI.ID.10 & 12, HS.F-IF.B.6, HS.F- IF.C.7, HS.F-LE.A.2): The student will understand that linear relationships can be described using multiple representations.

Today you will… Find the equation of a line when you are given the slope of the line and any point on the line.

Steps to write the equation in y = mx + b form given the slope and one point. 1.Write the equation y = mx + b 2.Plug the given slope into the m spot 3.Plug in the x and y values of the given point into the equation 4.Solve for b 5.Plug the solution into the equation for the b value.

Write an equation of the line that passes through the point (6,-3) with a slope of -2. Follow the steps: y = mx + b y = mx + b -3 = -2(6) + b (plug in m, x, and y) -3 = b (add 12 to both sides) 9 = b 9 = b y=-2x+9 (plug in the m and b value)

Graphic Check: y = -2x + 9 Note that the line crosses the y-axis at the point (0,9) and passes through the given point (6,-3). Note that the line crosses the y-axis at the point (0,9) and passes through the given point (6,-3). Use real graph paper and plug in (0,9) on the y-axis. Count down 2 back one until you cross (6,-3).

Find the equation of a line with a slope of 4 and a point of (8, 3) on the line. Follow the steps: y = mx + b y = mx + b 3 = 4(8) + b (plug in m, x, and y) 3 = 4(8) + b (plug in m, x, and y) 3 = 32 + b (subtract 32 from both sides) 3 = 32 + b (subtract 32 from both sides) -29 = b -29 = b y= 4x - 29 (plug in the m and b value) y= 4x - 29 (plug in the m and b value)

Real-life application Between 1980 and 1990 the number of vacations taken by Americans increased by about 15,000,000 per year. Between 1980 and 1990 the number of vacations taken by Americans increased by about 15,000,000 per year. In 1985 Americans went on 340,000,000 vacation trips. In 1985 Americans went on 340,000,000 vacation trips. Find an equation that gives the number of vacation trips, y (in millions), in terms of years, t. Find an equation that gives the number of vacation trips, y (in millions), in terms of years, t.

A Linear Model for Vacation Travel Question What is your slope? What is your given point? Solution It is your rate of change. The constant rate is 15 million trips/year, so m= 15 (5, 340) Where 5 represents represents the number of trips in millions

Now follow the steps and find the equation when m = 15 and the given point is (5, 340) So the slope-intercept form of the equation is y=15t+265 Follow the steps: y = mx + b y = mx + b 340 = 15(5) + b (plug in m, x, and y) 340 = 15(5) + b (plug in m, x, and y) 340 = 75 + b (subtract 75 from both sides) 340 = 75 + b (subtract 75 from both sides) 265 = b 265 = b y= 15x (plug in the m and b value) y= 15x (plug in the m and b value)