Question

Write an equation for the line that passes through (2,5) and (6,7)

Answer 1

The slope is the change in y over the change in x.

(7-5) / (6-2) = 2 / 4 = 1 / 2

In y = mx + b, we know y, m, and x. Now solve for b:

Let's use the point (2, 5).

5 = (1/2)(2) + b

5= 1 + b

b = 4

Now put it together:

y = (1/2)x + 4

Explanation:

Answer 2

`y=(1)/(2)x+4`

Explanation:

Find the slope of the line first using the slope formula:

• 
  `(y_2-y_1)/(x_2-x_1)`

Substitute the two given points into this formula.

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  `(7-5)/(6-2) =(2)/(4) =(1)/(2)`

Now that you have a slope and a point that the line passes through, you can use the point-slope formula to find the equation of the line.

Point-slope formula:

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  `y-y_1=m(x-x_1)`

Substitute m = 1/2 for the slope and one of the points; I'm going to use (2, 5).

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  `y-(5)=(1)/(2) (x-(2))`

Simplify the equation so it's easier to read.

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  `y-5=(1)/(2) (x-2)`

Distribute 1/2 inside the parentheses.

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  `y-5=(1)/(2)x-1`

Add 5 both sides of the equation.

• 
  `y=(1)/(2)x+4`