Is each line parallel, perpendicular, or neither parallel nor perpendicular to the line x + 2y = 6? Drag each choice into the boxes to correctly complete the table y= -1/2x+5 -2x+y=-4 -x+2y=2 x+2y=-2

2 answers
Question:

Is each line parallel, perpendicular, or neither parallel nor perpendicular to the line x + 2y = 6?
Drag each choice into the boxes to correctly complete the table
y= -1/2x+5
-2x+y=-4
-x+2y=2
x+2y=-2

Answers

y=-1/2x+5 is parallel.-2x+y=-4 is perpendicular.-x+2y=2 is neither.x+2y=2 is parallel.Hope this helps

ANSWERWe need to rewrite [tex]x+2y=6[/tex], in slope intercept form.[tex]\Rightarrow 2y=-x+6[/tex],[tex]\Rightarrow y=-\frac{1}{2}x+3[/tex]The given equation has a slope of [tex]-\frac{1}{2}[/tex].ANSWER TO QUESTION 1We now the write given options also in slope intercept form.For the first one, we have[tex]y=-\frac{1}{2}x+5[/tex]This first equation also has a slope  of [tex]-\frac{1}{2}[/tex].Hence [tex]y=-\frac{1}{2}x+5[/tex] is parallel to [tex]x+2y=6[/tex].ANSWER TO QUESTION 2:The second equation is; [tex]-2x+y=-4[/tex].We need to write this one too in slope intercept form.[tex]y=2x-4[/tex]This second equation has a slope of 2Since [tex]2\times -\frac{1}{2}=-1[/tex], the line [tex]-2x+y=-4[/tex]is perpendicular to [tex]x+2y=6[/tex].ANSWER TO QUESTION 3We rewrite the equation [tex]-x+2y=2[/tex] in slope intercept form.[tex]\Rightarrow 2y=x+2[/tex][tex]\Rightarrow y=\frac{1}{2}x+1[/tex]This equation also has a slope of [tex]\frac{1}{2}[\tex]since the slope of [tex]-x+2y=2[/tex] is not equal to the slope of [tex]x+2y=6[/tex], and the product of these two slopes [tex]\frac{1}{2} \times - \frac{1}{2} \ne -1[/tex], the two lines are neither parallel nor perpendicular.QUESTION 4The given line has equation [tex]x+2y=-2[/tex]. We rewrite this equation in the slope intercept form.[tex]\Rightarrow 2y=-x-2[/tex][tex]\Rightarrow y=-\frac{1}{2}x-1[/tex]This line has a slope of [tex]-\frac{1}{2}[/tex]. Since this slope is the same as the slope of the given line, [tex]y=-\frac{1}{2}x-1[/tex] is parallel to  [tex]x+2y=6[/tex].See graph in attachment.

Similar Solved Questions

2 answers

The stock market crash of 1929 was direct result of

the stock market crash of 1929 was direct result of...
1 answer

Find c and graph the equation y–2.5x=c, if the graph passes through the point K(2,–3).

Find c and graph the equation y–2.5x=c, if the graph passes through the point K(2,–3)....
2 answers

Nosotros queremos _____ elegantemente este viernes.

Nosotros queremos _____ elegantemente este viernes....
2 answers

The solutions of a quadratic function are its y-intercepts. Ture or false

The solutions of a quadratic function are its y-intercepts. Ture or false...
2 answers

Amino acid is to protein as what is to what?

amino acid is to protein as what is to what?...
2 answers

Starch is a natural polymer composed of

Starch is a natural polymer composed of...
1 answer

Solve the equation simultaneously. Y=x² + 2x + 1, Y= x²+2x - 2.. Solve for the values of X and Y.​

solve the equation simultaneously. Y=x² + 2x + 1, Y= x²+2x - 2.. Solve for the values of X and Y.​...
1 answer

How many formula units are in 9.3 g of alumina (Al2O3)?

How many formula units are in 9.3 g of alumina (Al2O3)?...
1 answer

A jet flew from new york to london in 7 hours the average speed was 499.4 miles an hour how many miles was the trip

A jet flew from new york to london in 7 hours the average speed was 499.4 miles an hour how many miles was the trip...
1 answer

2. Explain what happens to the demand curve for apples as a consequence of each of the following: a. More people begin to prefer apples to oranges. b. The price of peaches rises (because peaches are a substitute for apples). c. People's incomes rise (and apples are a normal good).

2. Explain what happens to the demand curve for apples as a consequence of each of the following: a. More people begin to prefer apples to oranges. b. The price of peaches rises (because peaches are a substitute for apples). c. People's incomes rise (and apples are a normal good)....
1 answer

Which of the following was NOT a part of the Compromise of 1850??

Which of the following was NOT a part of the Compromise of 1850??...
1 answer

16x^2 - 49 when factored is ?

16x^2 - 49 when factored is ?...
1 answer

Suppose a and b are the solutions to the quadratic equation 2x^2-3x-6=0. Find the value of (a+2)(b+2).

Suppose a and b are the solutions to the quadratic equation 2x^2-3x-6=0. Find the value of (a+2)(b+2)....
1 answer

Which ratio represents cos x in the triangle to the right ?

Which ratio represents cos x in the triangle to the right ?...
1 answer

Consider the following four types of payments that could be made by a normal operating firm: interest, common dividends, income taxes, and preferred dividends. Compared to the other payments mentioned, where would you rank common dividend payments in terms of the order of payment if the firm is liquidating?

Consider the following four types of payments that could be made by a normal operating firm: interest, common dividends, income taxes, and preferred dividends. Compared to the other payments mentioned, where would you rank common dividend payments in terms of the order of payment if the firm is liqu...
1 answer

Which is the equation of the given line? x = 1 y = 2x y=x y=1 (need help ASAP)

Which is the equation of the given line? x = 1 y = 2x y=x y=1 (need help ASAP)...
1 answer

Diana and Alejo are a party organized by the international club. Complete the following conversation between them with the appropriate words. PLEASE HELP ASAP!!! 50 points!!

Diana and Alejo are a party organized by the international club. Complete the following conversation between them with the appropriate words. PLEASE HELP ASAP!!! 50 points!!...
1 answer

In its early years, Seattle was one of many villages on the Puget Sound that was known for this industry A. fishing B. mining C. logging D. computer

In its early years, Seattle was one of many villages on the Puget Sound that was known for this industry A. fishing B. mining C. logging D. computer...
2 answers

Pieces of DNA that code for particular traits that can be inherited

pieces of DNA that code for particular traits that can be inherited...
1 answer

A hockey player strikes a puck, giving it an initial velocity of 15.0 m/s in the positive x-direction. The puck slows uniformly to 6.20 m/s when it has traveled 45.0 m. (Take the direction of initial motion as the positive direction. Indicate the direction with the sign of your answer.) (a) What is the puck's acceleration? (b) At what velocity is it traveling after 2.80 s? (c) How long does it take to travel 45.0 m?

A hockey player strikes a puck, giving it an initial velocity of 15.0 m/s in the positive x-direction. The puck slows uniformly to 6.20 m/s when it has traveled 45.0 m. (Take the direction of initial motion as the positive direction. Indicate the direction with the sign of your answer.) (a) What is ...

-- 0.014229--