Answered

Discover the answers you need at Westonci.ca, a dynamic Q&A platform where knowledge is shared freely by a community of experts. Get detailed answers to your questions from a community of experts dedicated to providing accurate information. Get precise and detailed answers to your questions from a knowledgeable community of experts on our Q&A platform.

What is the point-slope form of a line with slope 6 that contains the point [tex]$(1,2)$[/tex]?

A. [tex]y - 2 = 6(x - 1)[/tex]

B. [tex]y + 2 = 6(x + 1)[/tex]

C. [tex]y + 2 = 6(x - 1)[/tex]

D. [tex]x + 1 = 6(y + 2)[/tex]

Sagot :

GinnyAnswer
To find the point-slope form of a line, we use the formula:

[tex]\[ y - y_1 = m(x - x_1) \][/tex]

where [tex]\((x_1, y_1)\)[/tex] is a given point on the line and [tex]\(m\)[/tex] is the slope.

Given the slope [tex]\(m = 6\)[/tex] and the point [tex]\((1, 2)\)[/tex], we can substitute these values into the formula:

1. Start with the point-slope formula:
[tex]\[ y - y_1 = m(x - x_1) \][/tex]

2. Substitute the slope [tex]\(m = 6\)[/tex]:
[tex]\[ y - y_1 = 6(x - x_1) \][/tex]

3. Substitute the point [tex]\((x_1, y_1) = (1, 2)\)[/tex]:
[tex]\[ y - 2 = 6(x - 1) \][/tex]

Simplifying, we get the equation:
[tex]\[ y - 2 = 6(x - 1) \][/tex]

Thus, the point-slope form of the line with slope [tex]\(6\)[/tex] passing through the point [tex]\((1, 2)\)[/tex] is:

[tex]\[ y - 2 = 6(x - 1) \][/tex]

So, the correct option is:

A. [tex]\( y - 2 = 6(x - 1) \)[/tex]
Thanks for using our service. We aim to provide the most accurate answers for all your queries. Visit us again for more insights. Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. Westonci.ca is your trusted source for answers. Visit us again to find more information on diverse topics.