1.1 writing linear equations

1.1 Writing Linear Equations

Finding SlopeSlope-Intercept Form

Point-Slope Form

Finding Slope

Example 1: Finding Slope by Using the Slope FormulaFind the slope of the line that contains (2, 5) and (8, 1).

Use the slope formula.

Substitute (2, 5) for (x1, y1) and (8, 1) for (x2, y2).

Simplify.

The slope of the line that contains (2, 5) and (8, 1)

is .

Slope

Find the slope of the line that contains (–2, –2) and (7, –2).Check It Out! Example 1a

Use the slope formula.

Substitute (–2, –2) for (x1, y1) and (7, –2) for (x2, y2).

Simplify.

The slope of the line that contains (–2, –2) and (7, –2) is 0.

= 0

Slope

Find the slope of the line that contains (5, –7) and (6, –4).Check It Out! Example 1b

Use the slope formula.

Substitute (5, –7) for (x1, y1) and (6, –4) for (x2, y2).

Simplify.

The slope of the line that contains (5, –7) and (6, –4) is 3.

= 3

Slope

Example 2A: Finding Slope from Graphs and TablesThe graph shows a linear relationship. Find the slope.

Let (0, 2) be (x1, y1) and (–2, –2) be (x2, y2).

Simplify.

Use the slope formula.

Substitute (0, 2) for (x1, y1) and (–2, –2) for (x2, y2).

Slope

Check It Out! Example 2a

The graph shows a linear relationship. Find the slope.

Simplify.

Use the slope formula.

Let (2, 2) be (x1, y1) and (4, 3) be (x2, y2).

Substitute (2, 2) for (x1, y1) and (4, 3) for (x2, y2).

Slope

Check It Out! Example 2b

Simplify.

Use the slope formula.

Let (–2, 4) be (x1, y1) and (0, –2) be (x2, y2).

Substitute (–2, 4) for (x1, y1) and (0, –2) for (x2, y2).

The graph shows a linear relationship. Find the slope.

Slope

As shown in the previous examples, slope can be positive, negative, zero or undefined. You can tell which of these is the case by looking at a graph of a line–you do not need to calculate the slope.

Slope

Example 4: Finding Slopes of Horizontal and Vertical Lines

Find the slope of each line.

You cannot divide by 0

The slope is undefined. The slope is 0.

A. B.

Slope

Slope-Intercept Form

Holt Algebra 2

2-4 Writing Linear Functions Example 1: Writing the Slope-Intercept Form of the

Equation of a LineWrite the equation of the graphed line in slope-intercept form.

Step 1 Identify the y-intercept.The y-intercept b is 1.

Holt Algebra 2

2-4 Writing Linear Functions Example 1 Continued

Step 2 Find the slope.Choose any two convenient points on the line, such as (0, 1) and (4, –2). Count from (0, 1) to (4, –2) to find the rise and the run. The rise is –3 units and the run is 4 units.

Slope is = = – . riserun

–34

34

3

–44

–3

Holt Algebra 2

2-4 Writing Linear Functions Example 1 Continued

Step 3 Write the equation in slope-intercept form.

y = mx + b

34y = – x + 1 m = – and b = 1. 3

4

The equation of the line is 34y = – x + 1.

Holt Algebra 2

2-4 Writing Linear Functions

Write the equation of the graphed line in slope-intercept form.

Step 1 Identify the y-intercept.The y-intercept b is 3.

Check It Out! Example 1

Holt Algebra 2

2-4 Writing Linear Functions

Step 2 Find the slope.Choose any two convenient points on the line, such as (–4, 0) and (0, 3). Count from (–4, 0) to (0, 3) to find the rise and the run. The rise is 3 units and the run is 4 units

Check It Out! Example 1 Continued

3

Slope is = . riserun

34

3 4 4

3

Holt Algebra 2

2-4 Writing Linear Functions

Step 3 Write the equation in slope-intercept form.

Check It Out! Example 1 Continued

y = mx + b

34y = x + 3 m = and b = 3. 3

4

The equation of the line is 34y = x + 3.

Point-Slope Form

Holt Algebra 1

5-7 Point-Slope FormExample 4A: Using Two Points to Write an EquationWrite an equation in slope-intercept form for the line through the two points.(2, –3) and (4, 1)Step 1 Find the slope.

Step 2 Substitute the slope and one of the points into the point-slope form.

Choose (2, –3).

y – y1 = m(x – x1)y – (–3) = 2(x – 2)

Holt Algebra 1

5-7 Point-Slope Form

Step 3 Write the equation in slope-intercept form.

y = 2x – 7–3 –3

Example 4A ContinuedWrite an equation in slope-intercept form for the line through the two points.(2, –3) and (4, 1)

y + 3 = 2(x – 2)y + 3 = 2x – 4

Holt Algebra 1

5-7 Point-Slope FormExample 4B: Using Two Points to Write an Equation

Write an equation in slope-intercept form for the line through the two points.(0, 1) and (–2, 9)Step 1 Find the slope.

Step 2 Substitute the slope and one of the points into the point-slope form.

Choose (0, 1).y – y1 = m(x – x1)y – 1 = –4(x – 0)

Holt Algebra 1

5-7 Point-Slope FormExample 4B Continued

Write an equation in slope-intercept form for the line through the two points.(0, 1) and (–2, 9)

Step 3 Write the equation in slope-intercept form.

y = –4x + 1+ 1 +1

y – 1 = –4(x – 0)y – 1 = –4x

Holt Algebra 1

5-7 Point-Slope FormCheck It Out! Example 4a

Write an equation in slope-intercept form for the line through the two points.(1, –2) and (3, 10)

Step 1 Find the slope.

Step 2 Substitute the slope and one of the points into the point-slope form.

Choose (1, –2).

y – y1 = m(x – x1)y – (–2) = 6(x – 1)

y + 2 = 6(x – 1)

Holt Algebra 1

5-7 Point-Slope FormCheck It Out! Example 4a Continued

Write an equation in slope-intercept form for the line through the two points.

Step 3 Write the equation in slope-intercept form.

y + 2 = 6x – 6– 2 – 2

y = 6x – 8

(1, –2) and (3, 10)

y + 2 = 6(x – 1)

Holt Algebra 1

5-7 Point-Slope FormCheck It Out! Example 4b

Write an equation in slope-intercept form for the line through the two points.(6, 3) and (0, –1)

Step 1 Find the slope.

Step 2 Substitute the slope and one of the points into the point-slope form.

Choose (6, 3).

y – y1 = m(x – x1)

Holt Algebra 1

5-7 Point-Slope FormCheck It Out! Example 4b Continued

Step 3 Write the equation in slope-intercept form.

+ 3 +3

Write an equation in slope-intercept form for the line through the two points.(6, 3) and (0, –1)

More ExamplesExample 1

Step 2: Find the slope.

More ExamplesExample 1 Continued

Notice how they gave you the y-intercept.

That means we can use slope-intercept form.

More ExamplesExample 2

Step 2: Find the slope.

More ExamplesExample 2 Continued

Notice how they didn’t give you the y-intercept.

That means we have to use point-slope form

More ExamplesExample 2 Continued

Now we need to simplify

Subtracting a negative is really adding

Add the 4 to both sides

+4 +4

More ExamplesExample 3 You Try Now

Write the equation of the lineSimply if needed

More ExamplesExample 4 You Try Now

Write the equation of the lineSimply if needed

More ExamplesAnswer Example 3

Step 2: Find the slope.

More ExamplesAnswer Example 3 Continued

Notice how they gave you the y-intercept.

That means we can use slope-intercept form.

More ExamplesAnswer Example 4

Step 2: Find the slope.

More ExamplesAnswer Example 4 Continued

Notice how they didn’t give you the y-intercept.

That means we have to use point-slope form

More ExamplesAnswer Example 4 Continued

Now we need to simplify

Subtracting a negative is really adding

Subtract the 14.2 from both sides-14.2 -14.2