write the equation in slope-intercept form of a line that passes through the given points: (1,2) and (3,-1)?

Answer 1

slope = change in y's / change in x's
slope = (-1 - 2) / (3 - 1)
slope = (-3) / (2)
slope = -3/2
m = -3/2 (m represents the slope)

Pick a point - I'll pick: (1,2) and use it in this next equation with this new slope we found:
(y - y1) = m*(x - x1)

(y - 2) = -3/2*(x - 1) <--distribute the -3/2 to both factors.

y - 2 = (-3/2)x + 3/2 <---Now get it into the form y = mx + b
by isolating y.

y = (-3/2)x + 3/2 + 2
y = (-3/2)x + 7/2

Answer 2

Going from x=1 to x = 3 the y-value decreases by 3, from y =2 to y = -1.
The slope is therefore -3/2.
The y-intercept can now be found.
Take the y-value at (1,2) and run it back onto the y-axis: 2 -1*(-3/2) = 3.5.
The eqn is thus
y = -1.5x + 3.5
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Answer 3

slope is dy/dx = -3/2, so plug in (1,2):
2 = (-3/2)(1) + b
2 = -3/2 + b
7/2 = b

y = (-3/2)x + 7/2

Answer 4

y = mx + b
m = (change in y)/(change in x)
m = (-1 - 2)/(3 - 1) = -3/2
y = (-3/2)x + b

use one of the points to find b, the intercept
2 = (-3/2)(1) + b
b = 7/2

y = (-3/2)x + 7/2