Standard Form of Linear Equations

Show your work for each problem.

1.
Which equation is in standard form?
1. a)
2. b)
3. c)
4. d)
Answer:
is in standard form with , , . All coefficients are integers and .
2.
In the equation , what is the value of ?
1. a)
2. b)
3. c)
4. d)
Answer:
In standard form , the coefficient of is . Here, means (including the negative sign).
3.
Find the y-intercept of . Enter just the number.
Answer: 5
Set : . The y-intercept is .
4.
Find the x-intercept of . Enter just the number.
Answer: 6
Set : . The x-intercept is .
5.
Convert to standard form.
1. a)
2. b)
3. c)
4. d)
Answer:
. Multiply by : . This is standard form with .
6.
Convert to standard form and find the value of C.
Answer: 8
. In standard form , we have .
7.
Convert to slope-intercept form.
Answer: y = -2x + 8
1. Isolate the y-term by subtracting 6x from both sides. What do you get? 3y = -6x + 24
2. Divide both sides by 3 to solve for y. What is the slope-intercept form? y = -2x + 8
8.
Find the x-intercept and y-intercept of .
Answer: (4, 0) and (0, -10)
1. To find the x-intercept, set y = 0. What is x? 4
2. To find the y-intercept, set x = 0. What is y? -10
9.
Which equation is NOT in proper standard form?
1. a)
2. b)
3. c)
4. d)
Answer:
has . Proper standard form requires . It should be .
10.
What is the slope of the line ? Enter as a fraction or integer.
Answer: -2
. The slope is .
11.
Write in standard form with integer coefficients.
Answer: 3x + 2y = 24
1. What is the LCD of 2 and 3? 6
2. Multiply the entire equation by 6. What is the result? 3x + 2y = 24
12.
Write an equation in standard form for the line through and .
Answer: 2x - y = 4
1. Calculate the slope using the two points. 2
2. Write in point-slope form using point (3, 2). y - 2 = 2(x - 3)
3. Expand and rearrange to standard form. 2x - y = 4
13.
If the line passes through the point , what is the value of ?
1. a)
2. b)
3. c)
4. d)
Answer:
Substitute : .
14.
A line in standard form has x-intercept and y-intercept . What is the value of ?
Answer: 9
Using : . Using : . So .
15.
Concert tickets cost 20 dollars for adults and 15 dollars for children. A group spent 200 dollars on tickets. Write an equation in standard form and find how many adult tickets were bought if there were 4 children.
Answer: 7
1. Write the cost equation in standard form. 20x + 15y = 200
2. Substitute y = 4 (children) into the equation. 20x + 60 = 200
3. Solve for x (adult tickets). 7
16.
Write an equation in standard form for the line with slope passing through .
Answer: 3x - 4y = 4
1. Write in point-slope form. y - 5 = (3/4)(x - 8)
2. Multiply both sides by 4 to eliminate the fraction. 4y - 20 = 3x - 24
3. Rearrange to standard form with A positive. 3x - 4y = 4
17.
What does the equation represent?
1. a)A point at
2. b)A line with slope 3
3. c)A vertical line at
4. d)A horizontal line at
Answer: A vertical line at
is a vertical line where x is always 4, regardless of y. This is standard form with .
18.
The lines and are the same line. What is ?
Answer: 24
The second equation is the first multiplied by 2: . So .