Question

Which equation describes this line?

(1, 13)101(2,4) 10 10 10
A. y-2 = 3(x-4)
B. y - 4 = 3 (x - 2)
C. y - 4 = 3(x + 2)
D. y- 1 = 3(x-13)

Answer 1

The given information seems to include two points, (1, 13) and (2, 4), which can be used to determine the equation of the line that passes through them. However, the sequence "101 10 10 10" is unclear and does not seem to relate directly to the question about the line's equation.

To find the equation of the line, we will use the two points to determine the slope and then use point-slope form to write the equation.

The slope
`(\( m \))` of a line passing through two points,
`\( (x_1, y_1) \)` and
`\( (x_2, y_2) \)`, is given by:

`\[ m = (y_2 - y_1)/(x_2 - x_1) \]`

Using the points (1, 13) and (2, 4):

`\[ m = (4 - 13)/(2 - 1) \]`

`\[ m = (-9)/(1) \]`

`\[ m = -9 \]`

Now that we have the slope, we can use the point-slope form of the equation for a line, which is:

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

Using point (1, 13):

`\[ y - 13 = -9(x - 1) \]`

Now we'll simplify this equation to match one of the given options:

`\[ y = -9x + 9 + 13 \]`

`\[ y = -9x + 22 \]`

None of the given options (A, B, C, D) have a slope of -9, which means either there was a mistake in the calculation, or the options provided do not match the points given. Let's double-check the calculation:

`\[ m = (4 - 13)/(2 - 1) = -9 \]`

If we made a mistake and the slope was positive 9, then the point-slope form with point (2, 4) would be:

`\[ y - 4 = 9(x - 2) \]`

This corresponds with option B. However, based on our calculation, the slope is -9, not 9. If you could provide clarity on the sequence "101 10 10 10" or confirm the points and the options, we could reassess the solution.