# Finding an Equation of a Line

• Oct 21st 2008, 10:34 AM
mjp1991
Finding an Equation of a Line
Find an equation in standard form of the line containing point P and having slope m.

1. P(2,1), m=2/3

2. P(-3,3), m=-4/3

Find an equation in standard form of the line having slope m and y-intercept b.

1. m=1, b=-3

2. m=-0.8, b=1.4

Find an equation in standard form of the line containing the given points.

1. (3,-2), (2,-3)

2. (4,-5), (1,-4)
• Oct 21st 2008, 11:53 AM
masters
Quote:

Originally Posted by mjp1991
Find an equation in standard form of the line containing point P and having slope m.

1. P(2,1), m=2/3

Standard form: ax + by = c

First, use the point-slope form to get an equation: $\displaystyle y - y_1 = m(x - x_1)$.
Then rearrange the equation to standard form.

y - 1 = 2/3(x - 2)
3y - 3 = 2x - 4
-2x + 3y = -1
2x - 3y = 1

2. P(-3,3), m=-4/3

This is done just like #1. See if you do it.

Find an equation in standard form of the line having slope m and y-intercept b.

1. m=1, b=-3

First, use the slope-intercept form to get an equation: y = mx + b
Then rearrange the equation to standard form.

y = 1x - 3
-x + y = -3
x - y = 3

2. m=-0.8, b=1.4

Just like #1

Find an equation in standard form of the line containing the given points.

1. (3,-2), (2,-3)

First, find the slope using $\displaystyle m=\frac{y_2-y_1}{x_2-x_1}$

$\displaystyle m=\frac{-3-^{-}2}{2-3}=\frac{-1}{-1}=1$

Next, use y = mx + b, use point (3, -2) and slope of 1 to find y-intercept b and to get an equation.

y = mx + b
-2 = 1(3) + b
-2 = 3 + b
-5 = b

Equation is y = x -5

Change to standard form:

-x + y = -5
x - y = 5

2. (4,-5), (1,-4)

Work it just like #1

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