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

User JHeni
by
8.6k points

2 Answers

5 votes

Answer:

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:

User Adriaan Koster
by
9.3k points
3 votes

Answer:


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.


  • (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:


  • 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).


  • y-(5)=(1)/(2) (x-(2))

Simplify the equation so it's easier to read.


  • y-5=(1)/(2) (x-2)

Distribute 1/2 inside the parentheses.


  • y-5=(1)/(2)x-1

Add 5 both sides of the equation.


  • y=(1)/(2)x+4
User Chengqi
by
8.6k points

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