Write Linear Equations & Understanding Slopes

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| By Coach Pitts

Coach Pitts

Community Contributor

Quizzes Created: 2 | Total Attempts: 1,343

Questions: 10 | Attempts: 345 | Updated: Mar 21, 2023

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Questions and Answers

1.

Write the equation in slope-Intercept form of the line that passes through the point (4,-6) and has a slope of -3/4?

Correct Answer
y = -3/4x - 3, y=-3/4x-3

Explanation
The equation is in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept. In this case, the slope is -3/4 and the point (4, -6) lies on the line. We can use the point-slope formula to find the equation: y - y1 = m(x - x1). Substituting the values, we get y - (-6) = (-3/4)(x - 4), which simplifies to y + 6 = (-3/4)x + 3. Rearranging the equation, we get y = (-3/4)x - 3, which matches the given answer.

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2.

Write the equation in slope-intercept form for the equation of the line that passes through the point (-5, -3/4) and has a slope of 1/20 ?

Correct Answer
y=1/20x-1/2, y=1/20x-2/4

Explanation
The equation in slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept. In this case, the slope is 1/20. To find the y-intercept, we can substitute the coordinates of the given point (-5, -3/4) into the equation and solve for b. By substituting the values, we get -3/4 = (1/20)(-5) + b. Simplifying this equation, we find that b = -1/2. Therefore, the equation in slope-intercept form for the line that passes through the point (-5, -3/4) with a slope of 1/20 is y = 1/20x - 1/2.

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3.

If point (-1,0) is on the line whose equation is y = -2x + b, what is the value of b?

Correct Answer
-2, b=-2

Explanation
The equation of the line is in the form y = mx + b, where m is the slope and b is the y-intercept. Since the point (-1,0) lies on the line, we can substitute the x and y coordinates into the equation to solve for b. Plugging in x = -1 and y = 0, we get 0 = -2(-1) + b. Simplifying this equation, we get 0 = 2 + b. To isolate b, we subtract 2 from both sides, giving us b = -2. Therefore, the value of b is -2.

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4
4.

Write the equation of the line that is // to the line y = -1/2x + 4 and passes through the point (-4, -4).Write your answer in slope-intercept form.

Correct Answer
y = -1/2x - 6, y=-1/2x-6

Explanation
The equation of a line can be written in slope-intercept form as y = mx + b, where m represents the slope and b represents the y-intercept. In this case, the given line is parallel to y = -1/2x + 4, which means it has the same slope of -1/2. Since the line passes through the point (-4, -4), we can substitute these values into the equation and solve for the y-intercept. Plugging in the values, we get -4 = -1/2(-4) + b. Simplifying this equation, we find that b = -6. Therefore, the equation of the line is y = -1/2x - 6.

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5.

Write the equation of the line perpendicular to the line 3x - 5y = -1 and passes through the point ( 3, -4).Write the answer in Standard form.

Correct Answer
5x + 3y = 3, 5x+3y=3

Explanation
The equation of a line perpendicular to 3x - 5y = -1 can be found by rearranging the equation into slope-intercept form (y = mx + b), where m is the slope. The slope of the given line is (3/5). The slope of a line perpendicular to this line will be the negative reciprocal of (3/5), which is (-5/3). Using the point-slope form of a line (y - y1 = m(x - x1)), we can substitute the values of the point (3, -4) and the slope (-5/3) to find the equation of the line. Simplifying the equation will give us the standard form: 5x + 3y = 3. Therefore, the correct answer is 5x + 3y = 3.

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4
6.

Equation 1 has a slope of -2/3, what would be the perpendicular slope for equation 2?
- A.
  
  -2/3
- B.
  
  2/3
- C.
  
  3/2
- D.
  
  -3/2
Correct Answer
C. 3/2

Explanation
The perpendicular slope for a given slope is the negative reciprocal of that slope. In this case, the given slope is -2/3. To find the perpendicular slope, we take the negative reciprocal of -2/3, which is 3/2. Therefore, the correct answer is 3/2.

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7.

Given the line x = -7/9, what would be slope of the the line perpendicular to this line?
- A.
  
  9/7
- B.
  
  -7/9
- C.
  
  0
- D.
  
  Underfined
Correct Answer
C. 0

Explanation
The slope of a line perpendicular to another line is the negative reciprocal of the slope of the original line. Since the original line has a slope of 0 (because it is a vertical line), the slope of the line perpendicular to it would be the negative reciprocal of 0, which is also 0.

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8.

The line x = -2 is what type of line
- A.
  
  Diagonal line going up
- B.
  
  Diagonal line going down
- C.
  
  Vertical line
- D.
  
  Horizontal line
Correct Answer
C. Vertical line

Explanation
The line x = -2 is a vertical line because it is parallel to the y-axis. In a Cartesian coordinate system, a vertical line has a constant x-coordinate and can intersect the y-axis at any point. Since x = -2 is a constant value for all y-values, it represents a vertical line.

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9.

The line x = -2 has what type of slope?
- A.
  
  Positive slope
- B.
  
  Negative slope
- C.
  
  Zero slope
- D.
  
  Undefined slope
Correct Answer
D. Undefined slope

Explanation
The line x = -2 has an undefined slope because a vertical line does not have a change in y-coordinate for any change in x-coordinate. The slope is typically defined as the change in y divided by the change in x, but since there is no change in x for this line, the slope cannot be calculated. Therefore, the slope is undefined.

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10.

The line 2x - 3y = -1/3 has what type of slope?
- A.
  
  Positive Slope
- B.
  
  Negative Slope
- C.
  
  Zero Slope
- D.
  
  Undefined Slope
Correct Answer
A. Positive Slope

Explanation
The given equation is in the form y = mx + b, where m represents the slope. In this case, we can rearrange the equation to y = (2/3)x + 1/9. Since the coefficient of x is positive (2/3), the slope is positive. Therefore, the correct answer is positive slope.

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Current Version
Mar 21, 2023

Quiz Edited by
ProProfs Editorial Team
Dec 14, 2016

Quiz Created by
Coach Pitts

Write Linear Equations & Understanding Slopes

Write the equation in slope-Intercept form of the line that passes through the point (4,-6) and has a slope of -3/4?

Write the equation in slope-intercept form for the equation of the line that passes through the point (-5, -3/4) and has a slope of 1/20 ?

If point (-1,0) is on the line whose equation is y = -2x + b, what is the value of b?

Write the equation of the line that is // to the line y = -1/2x + 4 and passes through the point (-4, -4).Write your answer in slope-intercept form.

Write the equation of the line perpendicular to the line 3x - 5y = -1 and passes through the point ( 3, -4).Write the answer in Standard form.

Equation 1 has a slope of -2/3, what would be the perpendicular slope for equation 2?

Given the line x = -7/9, what would be slope of the the line perpendicular to this line?

The line x = -2 is what type of line

The line x = -2 has what type of slope?

The line 2x - 3y = -1/3 has what type of slope?