What is the standard form equation of the line shown below?
graph of a line going through negative 1, 1 and 1, 4
−3x + 2y = 5
3x − 2y = −5
y − 4 = three halves(x − 1)
y = three halvesx + five halves

We can determine first the slope of the line as follows:

slope = y2-y1 / x2-x1
slope = 4 - 1 / 1 -(-1)
slope = 3 / 2

We use the slope-point form of a line to determine the equation. We do as follows:

y - y1 = m(x - x1)
y - 4 = 3/2(x - 1)
y = 3x/2 - 3/2 + 4
y = 3x/2 + 5/2

Therefore, the last option is correct.