Question

What is an equation of the line that passes through the points

(6,1) and (7,2)? Put your answer in fully reduced form.

Answer 1

Answer (assuming it can be in slope-intercept form):

y = x - 5

Explanation:

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

`m = ((2)-(1))/((7)-(6)) \\m = (2-1)/(7-6) \\m = (1)/(1) \\m = 1`

2) Now that we know the slope and at least one point the line crosses through, we can write an equation of the line in point-slope form, or
`y-y_1 = m (x-x_1)`. Substitute
`m`,
`x_1`, and
`y_1` for real values.

Since
`m` represents the slope, substitute 1 for it. Since
`x_1` and
`y_1` represent the x and y values of a point the line intersects, use any one of the given points (either one is fine, either way the equation will represent the same line) and substitute its x and y values into the equation. (I chose the point (6, 1), as seen below.) Finally, isolate y to put the equation in slope-intercept form.

`y-1 = 1(x-6)\\y -1 = x-6\\y = x -5`