Algebra 3.4 Equations Of A Line

Front 1

Slope-Intercpt Form

Back 1

An equation such as
y = 2x + 3 that is solved for y is said to be in slope-intercept form, because both thre slope and the y-intercept of the line can be read directly from the equation.

Front 2

The intercept in a slope-intercept form is the _________.

Back 2

y-intercept

Front 3

Why is the slope-intercept form the most useful form for a linear equation?

Back 3

Because, of the information derived from it, such as slope & y-intercept. It is also used by graphing calculatoes and the one that describes a linear function.

Front 4

Using the slope-intercept form to find equations of lines.

Back 4

If m = 2/3 and the y-intercept is -1, what is the equation of a line?

y = 2/3x - 1

Front 5

Using the slope and y-intercept to graph a line.

Back 5

1. write the equation in slope-intercept form if neccessary, by solving for y.

2. Identify the y-intercept (0,b) and graph this point.

3. Identify slope m of the line. Use geometric interpretation of slope (rise over run) to find another point on th graph by counting from the y-intercept.

4. join the two points with a line to obtain the graph.

Front 6

Writing an equation of a line by using the slope and any point on the line.

Back 6

Write an equation in slope-intercept form, of a line having a slope of 4 passing through the point (2,5)?

y = mx + b

5 = 4(2) + b
5 = 8 + b
-8 -8
-3 = b

y = 4m - 3

Front 7

Point-slope Form

Back 7

y - y1 = m (x - x1)

where,

m = slope
(x1, y1) is a given point on the line

Front 8

Using the point-slope form to write equations.

Back 8

Find an equation of a line with point (-2,4), with a slope of -3. Give answer in slope-intercept form.

The given point is (-2,4), so x1 = -2 and y1 = 4; m = -3

point-slope form
y - y1 = m(x - x1)
y - 4 = -3[x - (-2)]
y - 4 = -3(x + 2)
y - 4 = -3x - 6
+4 +4
y = -3x -2

Front 9

Find the equation of a line by using two points.

Back 9

You can use either slope-intercept form or point-slope form to find an equation of a line when two points on the line are known.

Front 10

Find and equation of the line through the points (-2,5) and (3,4). give the answer in slope-intercept form.

Back 10

First find the slope:

y2 - y1 4 - 5 -1
m = ______ = _____ = __
x2 - x1 3 - (-2) 5


Then,

( y - y1) = m(x - x1)
y - 5 = -1/5 [(x - (-2)]
y - 5 = -1/5x -2/5
y - 5 +5 = -1/5x - 2/5 + 5/1
y = -1/5x - 2/5 + 25/5
y = -1/5x + 23/5

Front 11

Linear Equation in standard form.

Back 11

Ax + By = C

where, A,B, and C are integers, A>0, B is not equal to 0

Front 12

x = k

Back 12

Verical line
m = undefined
x-intercept (k,0)

eg. x = 3

Front 13

y = k

Back 13

Horizontal line
m = 0
y-intercept (0,k)

eg. y = 3

Front 14

y = mx + b

Back 14

slope-intercept form
m = slope
y-intercept (0,B)

eg. y = 2/3x - 6

Front 15

y - y1 = m(x - x1)

Back 15

Point-slope form
m = slope
line pass through (x1, y1)

eg. y + 3 = 3/2 ( x - 2 )

Front 16

Ax = By = C

Back 16

Standard form
slope = -A/B
y-intercept is ( 0, C/B )
x-intercept is ( C/A, 0 )