Point slope form: y – y_{1} = m(x – x_{1})
To write an equation in point-slope form, you need two pieces of information:
- the slope
- a point on the line
You are given a point on the line, so no need to worry about that yet.
But you are not given the slope, so you need to find it.
Use slope formula: m = (y_{2} - y_{1})/(x_{2} - x_{1})
The two points you are given (-4,1) and (5,7) can be plugged into the formula.
(-4,1) = (x_{1}, y_{1})
(5,7) = (x_{2}, y_{2})
Plug in and solve for slope:
m = (7 - 1)/(5 - (-4))
m = 6/9
Slope = 6/9
Now, plug in that slope, and a point given (here, use (-4,1) because that's the one in the answer choices) into the slope-intercept formula:
y – y_{1} = m(x – x_{1})
y - 1 = (6/9)(x - (-4))
Simplifying,
y - 1 = (6/9)(x + 4)
None of the answer choices seem to match this answer - are there any typos in the question (for the points given or the answer choices)? If there were any typos in the points, you can use the steps above but plug in those points instead.
If there are no typos in the points, but typos in the answer choices, the answer would be:
y - 1 = (6/9)(x + 4)