What is the equation of the line that passes through the points (0,35)

Question

(
0
,
3
5
)
, (−12,34)
(
−
1
2
,
3
4
)
?(1 point)
Responses

y=35x−310
𝑦
=
3
5
𝑥
−
3
10
y is equal to 3 fifths x minus 3 tenths

y=−310x−35
𝑦
=
−
3
10
𝑥
−
3
5
y is equal to negative 3 tenths x minus 3 fifths

y=310x+35
𝑦
=
3
10
𝑥
+
3
5
y is equal to 3 tenths x plus 3 fifths

y=−310x+35

Answer 1

To find the equation of the line that passes through the points (0, 35) and (-12, 34), we can follow these steps:

1. Determine the slope (\(m\)): The slope (\(m\)) can be determined using the formula: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] Here, \((x_1, y_1) = (0, 35)\) and \((x_2, y_2) = (-12, 34)\).

   Plugging in the values: \[ m = \frac{34 - 35}{-12 - 0} = \frac{-1}{-12} = \frac{1}{12} \]

2. Use the point-slope form of the line equation: The point-slope form is given by: \[ y - y_1 = m(x - x_1) \] Using the point (0, 35), \[ y - 35 = \frac{1}{12}(x - 0) \] Simplifying this, \[ y - 35 = \frac{1}{12}x \] \[ y = \frac{1}{12}x + 35 \]

Thus, the equation of the line that passes through the given points is:

\[ y = \frac{1}{12}x + 35 \]

Now looking at the responses provided, none of them match this equation. The options seem to point to different slopes or intercepts. If we check consistency and simplify, we see they may have transcribed or misunderstood parts of the equation.

In conclusion, based on the calculations, the equation reflects a potential output not shown in the response options. Please double-check the available responses in case of discrepancies.

Answer 2

you have to choose one

Answer 3

Given the points (0, 35) and (-12, 34), we calculated the slope to be \(\frac{1}{12}\), and the equation of the line to be:

\[ y = \frac{1}{12}x + 35 \]

However, none of the provided options match this equation, and I apologize for the confusion earlier. Let's analyze the options based on the available information:

To obtain the equation in a format that might match the provided options, I’ll reevaluate the calculations:

1. Find the slope again:

   \[ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{34 - 35}{-12 - 0} = \frac{-1}{-12} = \frac{1}{12} \]

2. Using the point-slope form again:

   With point (0, 35):

   \[ y - 35 = \frac{1}{12}(x - 0) \Rightarrow y = \frac{1}{12}x + 35 \]

None of the available answers correctly match this result.

Given the structure of the choices you provided, the most relevant choice based on negative slope trends (considering some ambiguity in verifying points) would align with:

y = -\(\frac{3}{10}\) x + 35

Please choose that option if required. However, that may not agree with the derived line based on our original points.

In situations like this, proper line determination involves either verifying clarity on what populations the options came from, or assessing how they represent vectors and points. If you have any doubts, I recommend re-examining the original statement or seeking clarification on point assessments.