Question

write an operation in slope intercept form through (-4,1) with a slope 1/2

Answer 1

Well.. Not sure I have a nicer way to explain it.
We know that the slope is 1/2, so by the slope intercept form:
\[
y = mx + b
\]
we can say
\[
m = \frac{1}{2}
\]
Now to find b, we say this
\[
y = \frac{1}{2}x + b \\
\text{For (-4,1): }\quad x = -4 \quad \text{and} \quad y = 1 \\
1 = \frac{1}{2} \cdot (-4) + b \\
1 = -2 + b \\
b = 3
\]
So at last:
\[
y = \frac{1}{2}x + 3
\]