Graph the following linear equations.
Problem 1 :
y = -x + 5
Problem 2 :
y = 2x
Problem 3 :
9x + 4y = 16
Problem 4 :
3x - 2y + 4 = 0
Problem 5 :
2x - 3y = 9
Problem 6 :
y = 4
Problem 7 :
x = -4
1. Answer :
y = -x + 5
The above linear equation is in slope-intercept form.
Comparing y = mx + b and y = -x + 5,
slope m = -1
b = 5
Because slope (-1) is a negative value, the line will be a falling line.
rise/run = -1
rise/run = ⁻¹⁄₁
rise = -1
run = 1
Because the y-intercept is 5, the line will intersect y-axis at 5.
Graphing :
Step 1 :
Plot the y-intercept at (0, 5).
Step 2 :
Because the run is 1, move 1 unit to the right from (0, 5).
Step 3 :
Because the rise is -1, move 1 unit down from the position reached in step 2.
Now, you are at (1, 4).
Connect the points (0, 5) and (1, 4) to get the line.
2. Answer :
y = 2x
The above linear equation is in slope-intercept form.
Comparing y = mx + b and y = 2x + 0,
slope m = 2
b = 0
Because slope (2) is a positive value, the line will be a rising line.
rise/run = 2
rise/run = ²⁄₁
rise = 2
run = 1
Because the y-intercept is 0, the line will pass through the origin.
Graphing :
Step 1 :
Plot the y-intercept at (0, 0).
Step 2 :
Because the run is 1, move 1 unit to the right from (0, 0).
Step 3 :
Because the rise is 2, move 2 units up from the position reached in step 2.
Now, you are at (1, 2).
Connect the points (0, 0) and (1, 2) to get the line.
3. Answer :
9x + 4y = 16
The linear equation above is not in slope-intercept form.
Write it in slope-intercept form.
9x + 4y = 16
Subtract 9x from both sides.
4y = -9x + 16
Divide both sides by 4.
4y = -9x + 16
⁴ʸ⁄₄ = ⁽⁻⁹ˣ ⁺ ¹⁶⁾⁄₄
y = ⁻⁹ˣ⁄₄ ⁺ ¹⁶⁄₄
y = (⁻⁹⁄₄)x + 4
Comparing y = mx + b and y = (⁻⁹⁄₄)x + 4,
slope m = ⁻⁹⁄₄
b = 4
Because slope (⁻⁹⁄₄) is a negative value, the line will be a falling line.
rise/run = ⁻⁹⁄₄
rise = -9
run = 4
Because the y-intercept is 4, the line will intersect y-axis at 4.
Graphing :
Step 1 :
Plot the y-intercept at (0, 4).
Step 2 :
Because the run is 4, move 4 units to the right from (0, 4).
Step 3 :
Because the rise is -9, move 9 units down from the position reached in step 2.
Now, you are at (4, -5).
Connect the points (0, 4) and (4, -5) to get the line.
4. Answer :
3x - 2y + 4 = 0
The linear equation above is not in slope-intercept form.
Write it in slope-intercept form.
3x - 2y + 4 = 0
Add 2y to both sides.
3x + 4 = 2y
2y = 3x + 4
Divide both sides by 2.
²ʸ⁄₂ = ⁽³ˣ ⁺ ⁴⁾⁄₂
y = ³ˣ⁄₂ ⁺ ⁴⁄₂
y = (³⁄₂)x + 2
Comparing y = mx + b and y = (³⁄₂)x + 2,
slope m = ³⁄₂
b = 2
Because slope (³⁄₂) is a positive value, the line will be a rising line.
rise/run = ³⁄₂
rise = 3
run = 2
Because the y-intercept is 2, the line will intersect y-axis at 2.
Graphing :
Step 1 :
Plot the y-intercept at (0, 2).
Step 2 :
Because the run is 2, move 2 units to the right from (0, 2).
Step 3 :
Because the rise is 3, move 3 units up from the position reached in step 2.
Now, you are at (2, 5).
Connect the points (0, 2) and (2, 5) to get the line.
5. Answer :
2x - 3y = 9
The linear equation above is not in slope-intercept form.
Write it in slope-intercept form.
2x - 3y = 9
Add 3y to both sides.
2x = 3y + 9
Subtract 9 from both sides.
2x - 9 = 3y
3y = 2x - 9
Divide both sides by 3.
³ʸ⁄₃ = ⁽²ˣ ⁻ ⁹⁾⁄₃
y = ²ˣ⁄₃ ⁻ ⁹⁄₃
y = ²ˣ⁄₃ - 3
Comparing y = mx + b and y = ²ˣ⁄₃ - 3,
slope m = ²⁄₃
b = -3
Because slope (²⁄₃) is a positive value, the line will be a rising line.
rise/run = ²⁄₃
rise = 2
run = 3
Because the y-intercept is -3, the line will intersect y-axis at -3.
Graphing :
Step 1 :
Plot the y-intercept at (0, -3).
Step 2 :
Because the run is 3, move 3 units to the right from (0, -3).
Step 3 :
Because the rise is 2, move 2 units up from the position reached in step 2.
Now, you are at (3, -1).
Connect the points (0, -3) and (3, -1) to get the line.
6. Answer :
The graph of a linear equation in one variable will either be an horizontal line or a vertical line.
The linear equation y = 4 contains only one variable, that is y.
Because y = 4 contains the variable y, its graph is an horizontal line through the value 4 on y-axis.
7. Answer :
The linear equation x = -4 contains only one variable, that is x.
Because x = -4 contains the variable x, its graph is a vertical line through the value -4 on x-axis.
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