Question

Write the equation of a line in slope-intercept form passing through (4, 5) and (6, 8)

Answer 1

we will find the slope by using the slope formula:
slope(m) = (y2 - y1) / (x2 - x1)
(4,5) x1 = 4 and y1 = 5
(6,8) x2 = 6 and y2 = 8
now we sub
slope(m) = (8 - 5) / (6 - 4)
m = 3/2 ===> your slope
now we use y = mx + b form and solve for b
(4,5) x = 4 and y = 5
m = 3/2
now we sub
y = mx + b
5 = 3/2(4) + b
5 = 12/2 + b
5 = 6 + b
5 - 6 = b
-1 = b
so your line is : y = 3/2x - 1 ==> slope intercept form

Answer 2

Write the equation of a line in slope-intercept form that has a slope of -2 and passes through the point (2, -8).