Answered

Westonci.ca is the best place to get answers to your questions, provided by a community of experienced and knowledgeable experts. Discover reliable solutions to your questions from a wide network of experts on our comprehensive Q&A platform. Explore comprehensive solutions to your questions from a wide range of professionals on our user-friendly platform.

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]

We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. Thank you for visiting Westonci.ca. Stay informed by coming back for more detailed answers.