Question

A line includes the points (4,1) and (8, 2). What is its equation in slope-intercept form?

Answer 1

Answer:

$y = \frac{1}{4} x$  

Step-by-step explanation:

1) First, find the slope of the equation. Use the slope formula $m= \frac{y_2-y_1}{x_2-x_1}$. Substitute the x and y values of the given points into the formula and solve:

$m = \frac{(2)-(1)}{(8)-(4)} \\m = \frac{2-1}{8-4}\\m = \frac{1}{4}$

Thus, the slope is $\frac{1}{4}$.

2) Now, use the point-slope formula $y-y_1 = m (x-x_1)$ to write the equation in point-slope form (from there we can convert it to slope-intercept). Substitute values for $m$, $x_1$, and $y_1$.

Since $m$ represents the slope, substitute $\frac{1}{4}$ for it. Since $x_1$ and $y_1$ represent the x and y values of one point the line intersects, choose any of the given points (it doesn't matter which one, the end result will be the same) and substitute its x and y values into the formula as well. (I chose (4,1), as seen below.) Then, isolate y to put the equation in slope-intercept form and find the answer.

$y-(1) = \frac{1}{4} (x-4)\\y-1 = \frac{1}{4} x-1\\y = \frac{1}{4} x+0\\y=\frac{1}{4}x$