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Line a is parallel to line b and goes through the point (1,2). Line b goes through the point (3,1) and is perpendicular to line c whose equation is y=-2x+3. Find the y-intercept of line a.

 Jul 4, 2023
 #1
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First, we need to find the slope of line b. Since line c has a slope of -2, and lines b and c are perpendicular, the slope of line b must be the negative reciprocal of -2, which is 1/2.

Now, we know that line a is parallel to line b, so they have the same slope. Therefore, the slope of line a is also 1/2.

We can use the point-slope form of linear equations to find the equation of line a. The point-slope form is y-y1=m(x-x1), where m is the slope and (x1,y1) is a point on the line.

We know that the slope of line a is 1/2 and the point (1,2) is on the line, so we can plug these values into the point-slope form to get the equation of line a:

y-2=(1/2)(x-1)

y-2=x/2-1/2

y=x/2+1

To find the y-intercept, we can let x=0 and solve for y. When x=0, y=1, so the y-intercept of line a is 1.

Therefore, the answer is 1.

 Jul 4, 2023
 #2
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I'll try to help you as soon as possible...

 Jul 4, 2023
 #3
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here's a hint...try working backwards...

 Jul 4, 2023
 #4
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alright...

we know line (c)'s equation which is   y = -2x + 3   and we also know that line (c) is perpendicular to line (b) ...which means line (b)'s slope would be the 
reciprocal  of line (c)'s slope... we know line (c)'s slope is  -2  which means line (b)'s slope will be   1/2.... we also know that line (b) goes through  (3,1)...now we can easily find (b)'s equation

(y - 1) / (x - 3)  =  1 / 2 

simplifying this equation gives us....     2y - 2 = x - 3  which comes out to  y = 1x/2  - 1/2

now that we know the equation for line (b), we can easily find the equation of line (a), since line (a) is parallel to line (b) and we know line (a) goes through (1,2) , ... using the same process...

(y - 2) / (x - 1)  =  1/2

2(y - 2) = 1(x - 1)

2y - 4 = x - 1

2y = x + 3

y = 1x/2  +  3/2


now that we know what line (a)'s equation is, we can now find the y-intercept of line (a)

y = (0)/2 + 3/2     =    y = 3/2


therefore the y-intercept for line (a) is (3/2)


I hope this helps....

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 Jul 4, 2023
 #5
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thank you you too! :))

sheeshers  Jul 5, 2023

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