Question

Which equation in slope-intercept from represents the line that passes through (-1, 5) and (5, 8)

y= 1/2 x -11
y=-1/2 x +11/2
y= 1/2 x +11/2
y= -1/2 x -11/2

Answer 1

Slope-intercept form:

y = mx + b

"m" is the slope, "b" is the y-intercept (the y value when x = 0) or (0,y)

To find the slope, you can use the slope formula and plug in the two points:

(-1,5) = (x₁ , y₁)

(5,8) = (x₂ , y₂)

`m=(y_(2)-y_(1))/(x_(2)-x_(1))`

`m=(8-5)/(5-(-1))`

`m=(8-5)/(5+1) =(3)/(6) =(1)/(2)`

y = 1/2x + b

To find "b", plug in either of the points into the equation:

(5,8)

y = 1/2x + b

8 = 1/2(5) + b

8 = 5/2 + b Subtract 5/2 on both sides

8 - 5/2 = b Make the denominators the same in order to subtract them

16/2 - 5/2 = b

11/2 = b

`y = (1)/(2)x+(11)/(2)`

The 3rd option is your answer

Answer 2

y= 1/2 x +11/2

Explanation:

To find the slope

m = (y2-y1)/(x2-x1)

= (8-5)/(5--1)

= 3/(5+1)

= 3/6

= 1/2

Using point slope form of a line

y-y1 = m(x-x1)

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

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

Distribute

y-5 = 1/2x +1/2

Add 5 to each side

y = 1/2x + 1/2 + 5

Change 5 to 10/2

y = 1/2x + 1/2 + 10/2

y = 1/2x + 11/2