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

Write your answer using integers, proper fractions, and improper fractions in simplest form.

1 Answer

6 votes

Answer:


y = (1)/(4) x

Explanation:

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


m = ((2)-(1))/((8)-(4)) \\m = (2-1)/(8-4)\\m = (1)/(4)

Thus, the slope is
(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
(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) = (1)/(4) (x-4)\\y-1 = (1)/(4) x-1\\y = (1)/(4) x+0\\y=(1)/(4)x

User RyanMac
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