Graph a linear equation
Graph: 2x – 3y = -12
Solve for y so the equation looks like y = mx + b
- 3y = -2x – 12
2
y= x+4
3
Subtract 2x to both sides.
Divide by –3 to both sides.
Now we can choose values for x to find values for y.
XY
3 6
0 4
-3 2
2
y = (3) + 4
23
y = (0) + 4
3
y=2+4
y=4
PLOT
y=
2
(-3) + 4
3
y = -2 + 4
NOW GRAPH A LINE
y=2
y=6
Graph a linear equation
Graph: 3x – 4y = 8
Solve for y so the equation looks like y = mx + b
- 4y = -3x + 8
3
y= x–2
4
Subtract 3x to both sides.
Divide by –4 to both sides.
Now we can choose values for x to find values for y.
XY
3
4 1
y = (4) -2
4
0 -2 y = 3 (0) - 2
4
-4 -5
y=3-2
y = -2
PLOT
y=
3
(-4) - 2
4
y = -3 - 2
NOW GRAPH A LINE
y = -5
y=1
Graph a linear equation
Graph: 3x = 6
X=2
Missing a y term, so solve for x
Divide by 3
Now we can graph a line in which the value for x is 2 in all
coordinates.
Notice the line is vertical because
every coordinate on the line has an
x coordinate of 2.
(2, 6)
(2, 0)
(2, -5)
Graph a linear equation
Graph: -4y = 12
Y = -3
Missing a x term, so solve for y
Divide by -4
Now we can graph a line in which the value for y is -4 in all
coordinates.
Notice the line is horizontal
because every coordinate on the
line has a y coordinate of -4.
(-3, -4)
(0, -4)
(3, -4)
Graph a linear equation using x and y intercepts.
Graph: 2x – 3y = -12
Let x = 0
2(0) – 3y = -12
Now let y = 0
2x – 3(0) = -12
2x – 0 = -12
2x = -12
0 - 3y = -12
-3y = -12
y=4
x = -6
x intercept is (-6, 0)
y intercept is (0, 4)
PLOT
NOW GRAPH A LINE
Graph a linear equation using x and y intercepts.
Graph: -5x + 3y = -15
-5(0) + 3y = -15
Let x = 0
Now let y = 0
-5x + 3(0) = -15
-5x + 0 = -15
-5x = -15
0 + 3y = -15
3y = -15
y = -5
x=3
x intercept is (3, 0)
y intercept is (0, -5)
PLOT
NOW GRAPH A LINE
Graph a linear equation, by using y intercept and slope.
Graph: 2x – 3y = -12
Solve for y so the equation looks like y = mx + b
- 3y = -2x – 12
2
y= x+4
3
Subtract 2x to both sides.
Divide by –3 to both sides.
Now the equation is in y = mx + b form called slope y-intercept form.
2
m is the slope of the line 3 and b is the y-intercept (0, 4)
Now plot the y-intercept (0, 4)
2
The slope of the line is
so from the coordinate (0, 4)
3
go up 2 lines, then move right 3 lines and plot a 2nd point.
UP 2
RIGHT 3
NOW GRAPH A LINE
Graph a line given one point and the slope of the line.
Graph the line that passes through the point (-4, 5) and has a
slope of
3
.
5
Plot the point (-4, 5)
Now from the point (-4, 5) the slope is
3
,
5
so go down 3 lines and then right 5 lines.
DOWN 3
RIGHT 5
Now graph the line