Writing an Equation of a LineI can…. determine the equation of a line and/or graph a linear equation.

1-24-13 Unit 1 Basics of Geometry

Forms of a linear equation

Slope-intercept Form y = mx + b

Standard Form Ax + By = C

Point-Slope Form y – y1 = m(x – x

1)

The method used to write anequation of a line depends on the information aboutthe line that is available.

If given the slope and y-intercept,

use slope-intercept form.

5

Example

m = 5, b = 7

y = ___ x + ___7

If given the a point and the slope,

There are two methods that are both effective.

The time required and the number of stepsfor the two methods is comparable.

Know how to do both, but typically eitherwill work just fine.

If given the a point and the slope,

Method 1

use slope-intercept form.

Example

m = –2, contains (5, –8)

Step 1

Substitute –2 for m, 5 for x, and–8 for y; then simplify to find the value of b.

y = mx + b–8 = –2(5) + b–8 = –10 + b 2 = b

Step 2Substitute –2 for m, and 2 for b.

y = –2x + 2

If given the a point and the slope,

Method 2

use point-slope form.

Example

m = –2, contains (5, –8)

Substitute –2 for m, 5 for x1, and

–8 for y1; then simplify and solve

the equation for y .

y – y1 = m(x – x

1)

y – (– 8) = – 2(x – 5)

y + 8 = –2x + 10

y = –2x + 2

If given two points,

First, find the slope using the slope formula.

Example

contains (5, –8) and (2, 7)

2 1

2 1

y ym

x x

m = 7 – -8 2 – 5

m = 15 –3

m = –5

If given two points,

Then use the slope and EITHER point to worklike the previous example.

y – y1 = m(x – x

1)

y – 7 = – 5(x – 2)

y – 7 = –5x + 10

y = –5x + 17

m = –5, contains (5, –8) and (2, 7)