As the name suggests, point slope form needs a point of the line and the slope, so you can find the slope using the slope formula: [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
Plug the points into the formula: [tex]\frac{4-(-1)}{-3-4} =\frac{5}{-7}[/tex]
The slope of the line is -5/7. Since you know that you can cancel out option A.
Now you can plug the slope and point (-3,4) --note that you can use any point on the line but we are using (-3,4) since all of the answer choices use this point-- into the point slope form equation. The equation is y-y1 = m(x-x1).
Plug the point and slope in.
y-4 = -5/7(x-(-3))
Simplify.
y-4 = -5/7(x+3)
The option that fits this equation is option C, so that is your answer.
Answer is:
C
