Answer:
[tex]y+4 = -\frac{1}{3} (x-1)[/tex]
Step-by-step explanation:
1) First, find the slope of the line. Use the slope formula [tex]m = \frac{y_2-y_1}{x_2-x_1}[/tex] to find the slope. Substitute the x and y values of the given points into the formula and solve:
[tex]m = \frac{(-5)-(-4)}{(4)-(1)} \\m = \frac{-5+4}{4-1} \\m = \frac{-1}{3}[/tex]
So, the slope is [tex]-\frac{1}{3}[/tex].
2) Use the point-slope formula [tex]y-y_1 = m (x-x_1)[/tex] to write the equation of the line in point-slope form. Substitute values for [tex]m[/tex], [tex]x_1[/tex], and [tex]y_1[/tex] into the formula.
Since [tex]m[/tex] represents the slope, substitute [tex]-\frac{1}{3}[/tex] in its place. Since [tex]x_1[/tex] and [tex]y_1[/tex] represent the x and y values of one point on the line, choose any one of the given points (it doesn't matter which one) and substitute the x and y values of it into the formula. (I chose (1,-4), as seen below). This gives the equation of the line in point-slope form.
[tex]y-(-4) = -\frac{1}{3} (x-(1))\\y+4 = -\frac{1}{3} (x-1)[/tex]
