STANDARD 6 & 7:
GRAPHING AND WRITING LINEAR EQUATIONS
Slope-Intercept Form
Slope Intercept form is the easiest way to graph a linear equation.
"M" is the slope (or the steepness of the graph)
"B" is the y-intercept (where the graph crosses the y-axis).
To graph using y=mx +b, start by putting a point on the y-intercept.
Then, move depending on the slope. Remember that slope is rise/run. So move up if the slope is positive and over to the right. If the slope is negative move down and over to the right.
To put an equation in slope intercept form, use the algebraic properties of equality in order to isolate the y (or get the y by itself).
Example: Put 3y - 6x = 9 in slope-intercept form
3y - 6x = 9
+6x +6x addition property of equality
3y = 6x + 9
3 3 3 division property of equality
y = 3x + 12
The y-intercept is 12 and the slope is 3 or 3/1
Graph this by putting a point at (0, 12)
Then from (0, 12) move up three and over to the right one.
Check out this video for more information: http://www.virtualnerd.com/algebra-1/linear-equation-analysis/slope-intercept-form/slope-intercept-form-examples/slope-intercept-form-definition
"M" is the slope (or the steepness of the graph)
"B" is the y-intercept (where the graph crosses the y-axis).
To graph using y=mx +b, start by putting a point on the y-intercept.
Then, move depending on the slope. Remember that slope is rise/run. So move up if the slope is positive and over to the right. If the slope is negative move down and over to the right.
To put an equation in slope intercept form, use the algebraic properties of equality in order to isolate the y (or get the y by itself).
Example: Put 3y - 6x = 9 in slope-intercept form
3y - 6x = 9
+6x +6x addition property of equality
3y = 6x + 9
3 3 3 division property of equality
y = 3x + 12
The y-intercept is 12 and the slope is 3 or 3/1
Graph this by putting a point at (0, 12)
Then from (0, 12) move up three and over to the right one.
Check out this video for more information: http://www.virtualnerd.com/algebra-1/linear-equation-analysis/slope-intercept-form/slope-intercept-form-examples/slope-intercept-form-definition
X and Y Intercepts
Intercepts are where the graph crosses an axis. Think intercept = intersect.
To find the x-intercept:
1. Set y = 0
2. Evaluate/solve to find x
3. write as a coordinate point (x, 0)
To find the y-intercept:
1. Set x=0
2. Evaluate/solve to find y
3, write as a coordinate point (0,y)
Example: Find the x and y intercepts of the equation 3x + 4y = 12.
To find the x-intercept, set y = 0 and solve for x.
3x + 4( 0 ) = 12
3x + 0 = 12
3x = 12
x = 12/3
x = 4 (4,0)
To find the y-intercept, set x = 0 and solve for y.
3( 0 ) + 4y = 12
0 + 4y = 12
4y = 12
y = 12/4
y = 3 (0,3)
Therefore, the x-intercept is ( 4, 0 ) and the y-intercept is ( 0, 3 ).
To find the x-intercept:
1. Set y = 0
2. Evaluate/solve to find x
3. write as a coordinate point (x, 0)
To find the y-intercept:
1. Set x=0
2. Evaluate/solve to find y
3, write as a coordinate point (0,y)
Example: Find the x and y intercepts of the equation 3x + 4y = 12.
To find the x-intercept, set y = 0 and solve for x.
3x + 4( 0 ) = 12
3x + 0 = 12
3x = 12
x = 12/3
x = 4 (4,0)
To find the y-intercept, set x = 0 and solve for y.
3( 0 ) + 4y = 12
0 + 4y = 12
4y = 12
y = 12/4
y = 3 (0,3)
Therefore, the x-intercept is ( 4, 0 ) and the y-intercept is ( 0, 3 ).
Graphing Linear Inequalities
The Solution of a linear inequality includes all of the shaded area!
We graph linear inequalities the same way that we graph linear equations--There are only 2 differences!
Dotted vs Solid Line:
We graph linear inequalities the same way that we graph linear equations--There are only 2 differences!
Dotted vs Solid Line:
- Draw a solid line for < or >
- Or make a Dotted line the inequality sign is < or >
- Shade above the line if the inequality is greater than > or >
- Shade below the line if the inequality is less than < or <
How to verify a point on a line or determine if a point is a solution to the linear equation
A solution of a linear equation is any point (x,y)that lies on the line.
To determine if a point is a solution
or
to determine if a point lies on a line:
1. Write out the equation with a vertical line down the equals sign.
2. Substitute in the point (x, y) into the equation for x and y
3. evaluate/solve through
***if the left side = the right side of the equation, then the point is a solution. But if the left side does not equal the right side, then it is not a solution/not on the line.
Check out this video for examples worked out! http://www.virtualnerd.com/algebra-1/relations-functions/graphing-linear-equations/identifying-linear-equations/check-point-line-equation
To determine if a point is a solution
or
to determine if a point lies on a line:
1. Write out the equation with a vertical line down the equals sign.
2. Substitute in the point (x, y) into the equation for x and y
3. evaluate/solve through
***if the left side = the right side of the equation, then the point is a solution. But if the left side does not equal the right side, then it is not a solution/not on the line.
Check out this video for examples worked out! http://www.virtualnerd.com/algebra-1/relations-functions/graphing-linear-equations/identifying-linear-equations/check-point-line-equation
SLOPE
How to find the slope of a line that contains two points (x,y) and (x,y)
1. Label each coordinate (x1, y1) and (x2, y2)
2. Substitute them into the equation for m
3. Evaluate
Example: Find the slope of the line through (2,4) and (-5, -7)
(2, 4) (-5, -7)
x2, y2 x1, y1
m = (4 - -7) = (4 + 7) = 1 1 Slope is 11/7
(2 - -5) (2 + 5) 7
Watch this video about slope: http://www.virtualnerd.com/algebra-1/linear-equation-analysis/slope-rate-of-change/understanding-slope/slope-formula-definition
Point Slope Formula
How to Write the equation of a line, when given a point and the slope:
1. Write out the point-slope formula
2. substitute in the point (x,y) for x1 and y1 and substitute the slope in for m
3. distribute
4. isolate the y with inverse operations
5. simplify
Watch a video to see an example:
http://www.virtualnerd.com/algebra-1/linear-equation-analysis/point-slope-standard-form/point-slope-examples/point-slope-form-definition
See the example Below
1. Write out the point-slope formula
2. substitute in the point (x,y) for x1 and y1 and substitute the slope in for m
3. distribute
4. isolate the y with inverse operations
5. simplify
Watch a video to see an example:
http://www.virtualnerd.com/algebra-1/linear-equation-analysis/point-slope-standard-form/point-slope-examples/point-slope-form-definition
See the example Below
St6- Skip 3E & 3F | |
File Size: | 76 kb |
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Standard 7 practice | |
File Size: | 82 kb |
File Type: | png |