Question

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

Answer 1

Answer:

$y=\frac{1}{2}x+4$

Step-by-step explanation:

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

• $\frac{y_2-y_1}{x_2-x_1}$

Substitute the two given points into this formula.

• $\frac{7-5}{6-2} =\frac{2}{4} =\frac{1}{2}$

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).

• $y-(5)=\frac{1}{2} (x-(2))$

Simplify the equation so it's easier to read.

• $y-5=\frac{1}{2} (x-2)$

Distribute 1/2 inside the parentheses.

• $y-5=\frac{1}{2}x-1$

Add 5 both sides of the equation.

• $y=\frac{1}{2}x+4$

Answer 2

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

Step-by-step explanation: