2. a line goes through the points (8,9) and (-2,4) . (a) what is the slope of the line? show your work (b) write the equation of the line in point-slope form. show your work (c) write the equation of the line in slope-intercept form. show your work.

(a) Slope of line:
We are given two points: (8,9) and (-2,4)
Slope of line is calculated using the following rule:
m = (y2-y1) / (x2-x1) where:
y2 = 4, y1=9, x2=-2 and x1=8
Therefore:
slope of line = m = (4-9) / (-2-8) = 0.5

(b) Equation of line in point-slope form:
point-slope equation has the general formula: y-y1=m(x-x1)  where x1 and y1 are the coordinates of a given point on the line.
Choose any point that belongs to your line, let's say we'll take (8,9). Substitute with the values in the equation as follows:
y-9 = 0.5(x-8)
Note: You can write the equation using the other point. It will be also correct.

(c) Equation of line in slope-intercept form:
slope-intercept equation has the general formula: y = mx+c where c is the y-intercept
we have calculated m to be 0.5.
Choose any point that belongs to the line and substitute in the general equation to get c. Let's choose (-2,4) this time. Therefore:
y = mx+c
4 = 0.5(-2) + c
4 = -1 + c
c = 5
The equation of the line is:
y = 0.5x + 5