Answer (assuming it can be in slope-intercept form):
[tex]y =2x[/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]. Substitute the x and y values of the given points into the formula and solve:
[tex]m = \frac{(8)-(2)}{(4)-(1)} \\m = \frac{8-2}{4-1} \\m = \frac{6}{3} \\m = 2[/tex]
So, the slope is 2.
2) Now, 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 real values for [tex]m[/tex], [tex]x_1[/tex], and [tex]y_1[/tex].
Since [tex]m[/tex] represents the slope, substitute 2 in its place. Since [tex]x_1[/tex] and [tex]y_1[/tex] represent the x and y values of a point the line intersects, choose one of the given points (it doesn't matter which one, the results will equal the same thing) and substitute its x and y values into the formula as well. (I chose (1,2), as seen below.) Then, isolate y to put the equation in slope-intercept form ([tex]y = mx + b[/tex] format) and find the following answer:
[tex]y-(2) = 2 (x-(1))\\y-2 = 2(x-1)\\y -2 = 2x-2\\y = 2x+0\\y = 2x[/tex]
