Write an equation that is in slop-intercept form of the line that passes through the points: (-1/2, -1) and (3, 5/2).

Use your slope formula

(-1 - 2.5) / (-.5 - 3) = -3.5/-3.5 = 1

Pick a point, does not matter which one, will get the same answer and use your point slope equation

y - 2.5 = 1(x - 3)
y = x - .5
y = x - (1/2)

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

5/2-(-1)/(3-(-1/2)=
(7/2)/7/2 =1
so slope of the equation is 1.
No substitute one of the points into point slope equation and solve into slope intercept form:
y-y1 =m(x-x1)
y-(-1)=1(x-(-1/2)
y+1=x+1/2
y = x-1/2

To write the equation of a line in slope-intercept form, we need two pieces of information: the slope of the line and the y-intercept.

We can find the slope using the formula:

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

Let's label our points:
Point 1: (-1/2, -1) with coordinates (x1, y1)
Point 2: (3, 5/2) with coordinates (x2, y2)

Substituting the coordinates into the slope formula, we get:

m = (y2 - y1) / (x2 - x1)
m = (5/2 - (-1)) / (3 - (-1/2))
m = (5/2 + 2/2) / (3 + 1/2)
m = (7/2) / (7/2)
m = 1

So, the slope (m) of the line passing through the two points is 1.

Next, we need to find the y-intercept (b). We can use the equation of a line: y = mx + b and substitute one of the points into the equation to solve for b.

We'll use point 1: (-1/2, -1) with coordinates (x1, y1):

y1 = mx1 + b
-1 = 1*(-1/2) + b
-1 = -1/2 + b
-1 + 1/2 = b
-2/2 + 1/2 = b
-1/2 = b

Therefore, the y-intercept (b) is -1/2.

Now that we have the slope (m) and the y-intercept (b), we can write the equation of the line in slope-intercept form, y = mx + b.

Substituting the values, we get:

y = 1x - 1/2

So, the equation of the line in slope-intercept form that passes through the points (-1/2, -1) and (3, 5/2) is y = x - 1/2.