4.7 Graphing Lines Using 4.7 Graphing Lines Using Slope Intercept FormSlope Intercept Form
Goal: Graph lines in slope intercept form.
Slope-Intercept Form of the Linear Equation
y = mx + bm
= slope
b
= y-interceptAny linear equation which is solved for y
is in slope-intercept form.
Find the Find the slopeslope and and y-intercepty-intercept of the of the following linear equations:following linear equations:
y = 3x + 4m = 3 b = 4
y = -2x - 1m = -2 b = -1
y = x -9 4
m = b =9 4
-2 1
-2 -1
y = 5x
m = 5 b = 0
Write a linear equation in the form y = mx + b given the following.
m = 2, b = -3
m = , b = 5
y = 2x - 32
32
53
y x
+3+2
-3
Graph the following linear equation using slope and y-intercept.
x
y
1) Find the slope and y-intercept.
Steps
2) Plot the y-intercept.
m = 23
or m = -2
4) Draw line through points.
y x 2
31
3
2m b 1
3) Plot the slope.-2
-3
+1
-3
Graph the line which passes through Graph the line which passes through (-2, 1) and has a slope of (-2, 1) and has a slope of -3-3.
x
y1) Plot the point.Steps
2) Write slope as fractionand count off other points.
m = -3 =-3
1or m =
3
-1
3) Draw line through points.
+4
+3
Graph the line which passes through (3, 2) and
has a slope of .
x
y
1) Plot the point.
Steps
2) Write slope as fractionand count off other points.
m = 34
or m = -3
-43) Draw line through points.
34
Write a linear equation in slope-intercept form
to describe each graph. y = mx + b
x
y
x
y
b = 3m 2
1y = 2x + 3
b = -43
1
m
y x 1
34
4
8
-62
Sometimes we must solve the equation for y before we can graph it.
2x y 3
2x y ( 2x) ( 2x) 3
y 2x 3
The constant, b = 3 is the y-intercept.
The coefficient, m = -2 is the slope.
1) Plot the y-intercept as a point on the y-axis. The constant, b = 3, so the y-intercept = 3.
2) Plot more points by counting the slope up the numerator (down if negative) and right the denominator. The coefficient, m = -2, so the slope = -2/1.
right 1down 2
right 1
down 2
y 2x 3
Parallel LinesGraph the following on the coordinate plane.
y x 1
23 y x
1
21
m 1
2
b 3
m 1
2
b 1x
y
Parallel lines have the same slope.
-3x -3x
Tell whether the lines below are parallel.
1) 3x + y = 7 y = -3x + 1
y = -3x + 7
m = -3
y = mx + b
m = -3
Lines are parallel!
Same slope!
