4-5A Writing Equations in Point-Slope Form

Algebra 1 Glencoe McGraw-Hill Linda Stamper

In today’s lesson you will write an equation given the slope and a point in point-slope form. To write an equation with this given information you will need to use the formula for point-slope form.

Memorize point-slope form 11 xxmyy

Read as: y minus y sub one equals m times the quantity of x minus x sub one.

11 xxmyy

Where does the point-slope form come from?

1 1

xxyym

).,yx( pair ordered an is point given the form, slope-point In 11

x

y 11 y,x The subscript identifies a specific

known point.It takes two points to determine a line. You do not know where the other point is located.In point-slope form, the unknown point will be represented by (x,y).

Write the slope formula.

22

location. known a identifiesonly subscript a because

x or y have not do You 22

•

•••

•

11

xxyym

Transform this formula by undoing the denominator.

11

xxyym

1xx 1xx

Simplify.

1

11 yym xx Use Symmetric Property to move everything to the other side of the equal sign.

m xxyy 11

Commute the m. 11 xxmyy

Start with the adjusted slope formula (no sub twos).

The result is point-slope form.

In order to use point-slope you must know the slope and one point.

How to write the equation of a line in point-slope form given one point and a graph.

2. Write the point-slope form.1. Find the slope by walking the line using slope ratio.

3. Substitute the given coordinate and the slope.

11 xxmyy

4. Simplify (undo double sign/double parentheses).

Write the equation of the line in the graph in point-slope form given the point (–2,–4).

x

y

m 52

(–2,–4)

11 xxmyy

y

2x254y

The equation is in point-slope form. Do not distribute the slope.

11 y,x ••

25m 25

4

x

2

Write the equation of the line in the graph in point-slope form using the given point.

x

y

m 21

(3,–1)

11 xxmyy

3x21y

3x21y

Do not distribute the slope.

11 y,x

2

••

Example 1 (3,–1)

Example 2 (-1,5)

x

y

m 31

(-1,5)

11 xxmyy

1x35y 1x35y

11 y,x

3

••

Write in point-slope form the equation of the line that passes through each point with the given slope.

11 xxmyy 1x57y

1x57y

Do not distribute the slope.

Example 3 (–1,–7), m = –5

Example 4 (–2,4), m = 3 11 xxmyy

2x34y 2x34y

Example 5 (–4,–3), m = –9 11 xxmyy 4x93y

4x93y

Example 6 (–2,0), m =

11 xxmyy

2x230y

2x23y

23

Write the equation of the line in the graph in point-slope form using the given point.

x

ym 0

(-3,3)

11 xxmyy

3x03y 03y

The slope of a horizontal line is 0.

•Example 7 (-3,3)

Example 8 (4,-2)

x

y0m

(4,-2)

11 xxmyy

4x02y 02y

•

x

y

time (hours)

dist

ance

(m

iles)

(2.5,162.5)

2550

1 2

•

Candace and her family are visiting her grandmother. After 2.5 hours in the car, they have traveled 162.5 miles. If the average speed of travel is 65 miles per hour, write the equation of the line in point-slope form.

0

75100125150175200225

3 4 5

Let x represent hours and y represent miles. The average speed of travel is the slope, so m = 65. Let = (2.5,162.5). 11 y,x

11 xxmyy 5.2x655.162y

5.2x655.162y

x

y

time (hours)

dist

ance

(m

iles)

(1.5,810)

100 1 2

•

Example 9 Charlie is flying from San Diego, California, to Washington D.C., for vacation. After 1.5 hours, his plane has traveled 810 miles. If the average speed of travel is 540 miles per hour, write the equation of the line in point-slope.

0

300

500

700

900

3 4 5

Let x represent hours and y represent miles.

11 xxmyy 5.1x540810y

5.1x540810y

4-A11 Pages 223-225 # 14–24,45,62-72.

Study Guide Page 56.