Which is an equation of the line containing the points (2,5) and (4,4) in standard form? a.) -2x + 5y = 12 b.)2x + y = 12 c.)x + 2y = 12 + 2y = 8

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Which is an equation of the line containing the points (2,5) and (4,4) in standard form? a.) -2x + 5y = 12 b.)2x + y = 12 c.)x + 2y = 12 + 2y = 8

the given points are:

(X1,Y1)=(2,5)

(X2,Y2)=(4,4)

Now the standard euation is,

Y-Y1=m(X-X1)

where m= ( Y2-Y1)/(X2_ X1)=(4-5)/(4-2)=-0.5

so

y-Y1= m( x- X1)

or, y-5=-0.5(x-2)

or, y-5=-0.5x+1

or, 0.5x+ y=1+5

or, x+2y=6×2

or, x+2y=12

This is the correct answer.

First, find the slope of the line thru these 2 pts:

5-4

m = = -1/2

2 -4

Use the slope-intercept formula y = mx + b:

5 = (-1/2)(2) + b. Then the y-intercept is 5 + 1, or 6: y = (-1/2)x + 6

Multiplying this entire result (3 terms) by 2 results in 2y = -x + 12, or

x + 2y = 12 (answer)

Slope m of the line = 5-4 / 2-4 = -1/2

using the point slope form of a line:-

y - y1 = m(x - x1) where (x1,y1) is a point on the line, we have:-

y - 5 = -1/2(x -2) using the point (2,5)

multiply through by 2:-

2y - 10 = -x + 2

x + 2y = 12 is the answer

x +2y = 12

Step-by-step explanation:

Try the given points in the given equations and see what works.

-2x + 5y at (2, 5) is -2(2) +5(5) = 21 ≠ 12

) +) 2x + y at (2, 5) = 2(2) +(5) = 9 ≠ 12

x + 2y at (2, 5) = 2 +2(5) = 12 . . . . . goes through first point

x + 2y at (4, 4) = 4 + 2(4) = 12 . . . . goes through second point

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You know the answer at this point, so the next check is just for "completeness." It is not necessary to properly answer the question.

-x +2y at (2, 5) = -(2) +2(5) = 8 . . . . goes through first point

-x +2y at (4, 4) = -(4) + 4(4) = 4 ≠ 8 . . . does not go through second point