5.2 Equations of Lines Given the

Slope and a Point

4 3 2 1 0

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 theteacher, the student haspartial 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-3 = -2(6) + b (plug in m, x,

and y)-3 = -12 + b (add 12 to both

sides) 9 = by=-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).

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 3 = 4(8) + b (plug in m, x, and

y) 3 = 32 + b (subtract 32 from both sides)

-29 = b 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.

• 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.

A Linear Model for Vacation TravelQuestion

What is your slope?

What is your given point?

SolutionIt is your rate of change. The constant rate is 15

million trips/year, so

m= 15

(5, 340)Where 5 represents 1985340 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 340 = 15(5) + b (plug in m, x,

and y) 340 = 75 + b (subtract 75 from both

sides)

265 = b y= 15x + 265 (plug in the m and b

value)