Answer (assuming it can be in slope-intercept form):
[tex]y = \frac{2}{3} x+\frac{5}{3}[/tex]
Step-by-step explanation:
1) Find the slope of the line by using the slope formula, [tex]m = \frac{y_2-y_1}{x_2-x_1}[/tex]. Substitute the x and y values of the given points into the equation and solve:
[tex]m = \frac{(3)-(1)}{(2)-(-1)} \\m =\frac{3-1}{2+1}\\m = \frac{2}{3}[/tex]
So, the slope is [tex]\frac{2}{3}[/tex].
2) Now, use the point-slope formula [tex]y-y_1 = m (x-x_1)[/tex] to write an equation of a line. Substitute values for [tex]m[/tex], [tex]x_1[/tex], and [tex]y_1[/tex].
Since [tex]m[/tex] represents the slope, substitute [tex]\frac{2}{3}[/tex] in its place. Since [tex]x_1[/tex] and [tex]y_1[/tex] represent the x and y values of one point the line intersects, substitute the x and y values of one of the given points (either one is fine, either choice will represent the same line) into the formula as well. (I chose (2,3) as seen below.) Then, with the resulting equation, isolate y to convert the equation into slope-intercept form:
[tex]y-(3) = \frac{2}{3} (x-(2))\\y-3 = \frac{2}{3} x-\frac{4}{3} \\y = \frac{2}{3} x-\frac{4}{3}+3\\ y = \frac{2}{3} x-\frac{4}{3} +\frac{9}{3}\\y = \frac{2}{3} x+\frac{5}{3}[/tex]
