Question
In the xy-plane, the graph of which of the following equations is perpendicular to the graph of the equation above?
- 3x +2y = 6
- 3x +4y = 6
- 2x +4y = 6
- 2x +6y = 3
Hint:
Hint:- The slope-intercept form of a straight line is used to find the equation of a line.
For the slope-intercept formula, we have to know the slope of the line and the intercept cut by the line with the y-axis.
Using the slope-intercept formula, the equation of the line is:
y = mx + b
where, m = the slope of the line
- b = y-intercept of the line
- (x, y) represent every point on the line
x and y have to be kept as the variables while applying the above formula.
x and y have to be kept as the variables while applying the above formula.
The correct answer is: 3x +2y = 6
Solution:- Option A) 3x +2y =6 is correct.
- The equation −2x + 3y = 6 can be rewritten in the slope-intercept form as follows:
y = (2/3)x + 2.
- Comparing with the standard equation y = mx+ c
So the slope of the graph of the given equation is 2/3
- In the xy-plane, when two nonvertical lines are perpendicular, the product of their slopes is −1. So, if m is the slope of a line perpendicular to the line with equation
y = (2/3)x+ 2, then m × (2/3)= −1,
- which gives
m = -3/2
- Of the given choices, only the equation in choice A can be rewritten in the form
y = -(-3/2) x +b, for some constant b.
- Therefore, the graph of the equation in choice A is perpendicular to the
graph of the given equation.
- Options B, C, and D are incorrect because the graphs of the equations in these choices have slopes, respectively, of -3/4 ,-1/2 , and -1/3 but not -3/2.
- Therefore correct option is A)3x +2y =6
The slope-intercept form is one of the most common ways to represent a line's equation. For example, the slope of a straight line, slope-intercept, and y-intercept formula determine the equation of a line (where the line intersects the y-axis at the point of the y-coordinate). An equation must be satisfied by each point on a line. For example, the graph of the linear equation y = mx + c is a line with slope m and y-intercept m and c. This is known as the slope-intercept form of the linear equation, and the values of m and c are real numbers.
¶A line's slope, m, represents its steepness. Sometimes the slope of a line is referred to as the gradient. A line's y-intercept, b, represents the y-coordinate of the point where the line's graph intersects the y-axis.
Related Questions to study
Alan drives an average of 100 miles each week. His car can travel an average of 25 miles per gallon of gasoline. Alan would like to reduce his weekly expenditure on gasoline by $5. Assuming gasoline costs $4 per gallon, which equation can Alan use to determine how many fewer average miles, m, he should drive each week?
To calculate average miles, divide the total distance traveled by the time spent traveling. This will provides us with your average speed.
So, for example, if Ben traveled 150 miles in 3 hours, 120 miles in 2 hours, and 70 miles in an hour, his average speed was about 57 miles per hour. In this case, Alan can travel a hundred miles per week at 25 miles per gallon of gasoline to save $5 per week on gas, assuming gasoline costs $4 per gallon.
Alan drives an average of 100 miles each week. His car can travel an average of 25 miles per gallon of gasoline. Alan would like to reduce his weekly expenditure on gasoline by $5. Assuming gasoline costs $4 per gallon, which equation can Alan use to determine how many fewer average miles, m, he should drive each week?
To calculate average miles, divide the total distance traveled by the time spent traveling. This will provides us with your average speed.
So, for example, if Ben traveled 150 miles in 3 hours, 120 miles in 2 hours, and 70 miles in an hour, his average speed was about 57 miles per hour. In this case, Alan can travel a hundred miles per week at 25 miles per gallon of gasoline to save $5 per week on gas, assuming gasoline costs $4 per gallon.
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?
The diameter of a circle is also known as its measurement of the circle's edge, circumference, or perimeter.
As opposed to this, a circle's area indicates the space it occupies.
The circle circumference is the length when we cut it, open and draw a straight line from it.
Units like centimeters or meters are typically used to measure it.
The circle's radius is considered when applying the formula to determine the circumference of the circle.
Therefore, to calculate a circle's circumference, we must know its radius or diameter.
Therefore, the circumference of a circle formula is the circle perimeter or circumference is 2πR.
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π is a mathematical constant with an estimated value of 3.14 (to the nearest two decimal places).
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The diameter of a circle is also known as its measurement of the circle's edge, circumference, or perimeter.
As opposed to this, a circle's area indicates the space it occupies.
The circle circumference is the length when we cut it, open and draw a straight line from it.
Units like centimeters or meters are typically used to measure it.
The circle's radius is considered when applying the formula to determine the circumference of the circle.
Therefore, to calculate a circle's circumference, we must know its radius or diameter.
Therefore, the circumference of a circle formula is the circle perimeter or circumference is 2πR.
where,
R is the circle's radius.
π is a mathematical constant with an estimated value of 3.14 (to the nearest two decimal places).
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