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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]
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