Do NowFind the value of m.

1. 2.

3. 4.

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Target: SWBAT

Find the slope of a line.

3.7 Equations of lines in a coordinate plane

Target: SWBATGraph lines and write their equations in

slope-intercept and point-slope form.

The slope of a line in a coordinate planeis a number that describes the steepness of the line. Any two points on a line can be used to determine the slope.

Example 1A: Finding the Slope of a Line

Use the slope formula to determine the slope of the line.

Substitute (–2, 7) for (x1, y1) and (3, 7) for (x2, y2) in the slope formula and then simplify.

AB

Example 1B: Finding the Slope of a Line

Use the slope formula to determine the slope of each line. AC

Substitute (–2, 7) for (x1, y1) and (4, 2) for (x2, y2) in the slope formula and then simplify.

The slope is undefined.

Example 1C: Finding the Slope of a Line

Use the slope formula to determine the slope of each line.

AD

Substitute (–2, 7) for (x1, y1) and (–2, 1) for (x2, y2) in the slope formula and then simplify.

A fraction with zero in the denominator is undefined becauseit is impossible to divide by zero.

Remember!

Example 1D: Finding the Slope of a Line

Use the slope formula to determine the slope of each line.

CD

Substitute (4, 2) for (x1, y1) and (–2, 1) for (x2, y2) in the slope formula and then simplify.

Check It Out! Example 1

Use the slope formula to determine the slope of JK through J(3, 1) and K(2, –1).

Substitute (3, 1) for (x1, y1) and (2, –1) for (x2, y2) in the slope formula and then simplify.

One interpretation of slope is a rate of change. If y represents miles traveled and x represents time in hours, the slope gives

the rate of change in miles per hour.

Example 1A: Writing Equations In Lines

Write the equation of each line in the given form.

the line with slope 6 through (3, –4) in point-slope form

y – y1 = m(x – x1)

y – (–4) = 6(x – 3)

Point-slope form

Substitute 6 for m, 3 for x1, and -4 for y1.

Example 1B: Writing Equations In Lines

Write the equation of each line in the given form.

the line through (–1, 0) and (1, 2) in slope-intercept form

y = mx + b

0 = 1(-1) + b

1 = b

y = x + 1

Slope-intercept form

Find the slope.

Substitute 1 for m, -1 for x, and 0 for y.

Write in slope-intercept form using m = 1 and b = 1.

Example 1C: Writing Equations In Lines

Write the equation of each line in the given form.

the line with the x-intercept 3 and y-intercept –5 in point slope form

y – y1 = m(x – x1) Point-slope form

Use the point (3,-5) to find the slope.

Simplify.

Substitute for m, 3 for x1, and 0 for y1.

53

y = (x - 3)53

y – 0 = (x – 3)53

Check It Out! Example 1a

Write the equation of each line in the given form.

the line with slope 0 through (4, 6) in slope-intercept form

y = 6

y – y1 = m(x – x1)

y – 6 = 0(x – 4)

Point-slope form

Substitute 0 for m, 4 for x1, and 6 for y1.

Check It Out! Example 1b

Write the equation of each line in the given form.

the line through (–3, 2) and (1, 2) in point-slope form

y - 2 = 0

Find the slope.

y – y1 = m(x – x1) Point-slope form

Simplify.

Substitute 0 for m, 1 for x1, and 2 for y1.

y – 2 = 0(x – 1)

Graph each line.

Example 2A: Graphing Lines

The equation is given in the

slope-intercept form, with a

slope of and a y-intercept

of 1. Plot the point (0, 1) and

then rise 1 and run 2 to find

another point. Draw the line

containing the points.

(0, 1)

rise 1

run 2

Graph each line.

Example 2B: Graphing Lines

y – 3 = –2(x + 4)

The equation is given in the

point-slope form, with a slope

of through the point (–4, 3).

Plot the point (–4, 3) and then

rise –2 and run 1 to find

another point. Draw the line

containing the points.

(–4, 3)

rise –2

run 1

Graph each line.

Example 2C: Graphing Lines

The equation is given in the form

of a horizontal line with a

y-intercept of –3.

The equation tells you that the

y-coordinate of every point on the

line is –3. Draw the horizontal line

through (0, –3).

y = –3

(0, –3)

Check It Out! Example 2a

Graph each line.

y = 2x – 3

The equation is given in the

slope-intercept form, with a

slope of and a y-intercept

of –3. Plot the point (0, –3)

and then rise 2 and run 1 to

find another point. Draw the

line containing the points.

(0, –3)

rise 2

run 1

Check It Out! Example 2b

Graph each line.

The equation is given in the

point-slope form, with a slope

of through the point (–2, 1).

Plot the point (–2, 1)and then

rise –2 and run 3 to find

another point. Draw the line

containing the points.

(–2, 1)

run 3

rise –2

Check It Out! Example 2c

Graph each line.

y = –4

The equation is given in the form

of a horizontal line with a

y-intercept of –4.

The equation tells you that the

y-coordinate of every point on the

line is –4. Draw the horizontal line

through (0, –4).

(0, –4)

Assignment #29 - Pages 194-196

Foundation – (9-15 odd, 16-22 even, 25-31 odd)

Core – (38, 39, 45, 47, 56)

Challenge - (58)