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What is an equation of the line that passes through the points
(6,1) and (7,2)? Put your answer in fully reduced form.

Sagot :

cosmickid287

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

y = x - 5

Step-by-step explanation:

1) First, find the slope of the equation. Use the slope formula, [tex]m = \frac{y_2-y_1}{x_2-x_1}[/tex], and substitute the x and y values of the given points into it. Then, solve:

[tex]m = \frac{(2)-(1)}{(7)-(6)} \\m = \frac{2-1}{7-6} \\m = \frac{1}{1} \\m = 1[/tex]

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 [tex]y-y_1 = m (x-x_1)[/tex]. Substitute [tex]m[/tex], [tex]x_1[/tex], and [tex]y_1[/tex] for real values.

Since [tex]m[/tex] represents the slope, substitute 1 for it. Since [tex]x_1[/tex] and [tex]y_1[/tex] 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.

[tex]y-1 = 1(x-6)\\y -1 = x-6\\y = x -5[/tex]

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