do now find the value of m. 1.2. 3.4. undefined0
TRANSCRIPT
Do NowFind the value of m.
1. 2.
3. 4.
undefined 0
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)