Equations For Lines

ObjectiveThe student will be able to:

1) write equations using slope-intercept form.

2) identify slope and y-intercept from an equation.

y = mx + bThe equation is called the slope intercept

form for a line.The graph of this equation is a straight

line.The slope of the line is m.The line crosses the y-axis at b.The point where the line crosses the y-

axis is called the y-intercept.The (x,y) coordinates for the y-intercept

are (0,b)

Y = mx+ bIf your slope is positive the line will go up

hill.If your slope is negative the line will go

down hill.Remember we read from left to right.Also, the slope is the m value.Slope is RISE over RUN written as a

fraction. If the m is a whole number put it over one

to form a fraction.

Types of lines1. All lines are straight.2. They can be horizontal, vertical, or

diagonal.

Graphing lines using the equation Identify the Y-intercept (b) and graph

it on the y-axis with a point. Identify what the slope is (m).

Remember slope is rise over run. From the point on the y-axis, if your

slope is positive go up or if it is negative go down whatever the RISE is. Go over to the right for the run. Mark the spot with a point.

Draw a line thru those two points

This is one of the big concepts in Algebra 1. You need to

thoroughly understand this!Slope – Intercept Form

y = mx + bm represents the slope

b represents the y-intercept

When asked to write an equation, you need to know two things – slope (m) and y-intercept (b).

There are three types of problems you will face.

Write an equation in slope-intercept form of the line that has a slope of 2 and a y-intercept of 6.

To write an equation, you need two things:slope (m) =y – intercept (b) =

We have both!! Plug them into slope-intercept form

y = mx + b

26

y = 2x + 6

Write the equation of a line that has a y-intercept of -3 and a slope of -4.1. y = -3x – 42. y = -4x – 33. y = -3x + 44. y = -4x + 3

Write an equation of the line that has a slope of 3 and goes through the point (2,1).

To write an equation, you need two things:slope (m) =y – intercept (b) =

We have to find the y-intercept!! Plug in the slope and ordered pair into

y = mx + b

3???

1 = 3(2) + b

1 = 3(2) + bSolve the equation for b

1 = 6 + b -6 -6

-5 = bTo write an equation, you need two things:

slope (m) =y – intercept (b) =

y = 3x - 53-5

Writing Equations – Type #3Write an equation of the line that goes through

the points (-2, 1) and (4, 2). To write an equation, you need two things:

slope (m) =y – intercept (b) =

We need both!! First, we have to find the slope. Plug the points into the slope formula.

Simplify 2 14 ( 2)

m

16

m

??????

Writing Equations – Type #3Write an equation of the line that goes through the

points (-2, 1) and (4, 2). To write an equation, you need two things:

slope (m) =y – intercept (b) =

It’s now a Type #2 problem. Pick one of the ordered pairs to plug into the equation. Which one looks easiest to use?

16

???

2 = (4) + bSolve the equation for b

2 = + b

b = 4/3

To write an equation, you need two things:slope (m) =y – intercept (b) = 4/3

16

23

23

23

16

Write an equation of the line that goes through the points (0, 1) and (1, 4).

1. y = 3x + 42. y = 3x + 13. y = -3x + 44. y = -3x + 1

To find the slope and y-intercept of an equation, write the equation in slope-intercept form: y = mx + b.

Find the slope and y-intercept.1) y = 3x – 7 y = mx + b

m = 3, b = -7

Find the slope and y-intercept.2) y = x y = mx + b y = x + 0

3) y = 5 y = mx + b

y = 0x + 5

23

23 m =

b = 023

m = 0b = 5

-3 -3 -3

Find the slope and y-intercept.4) 5x - 3y = 6

Write it in slope-intercept form. (y = mx + b)

5x – 3y = 6 -3y = -5x + 6

y = x - 253

53

m =

b = -2

Find the slope and y-intercept of y = -2x + 4

1. m = 2; b = 42. m = 4; b = 23. m = -2; b =

44. m = 4; b = -

2