Question

What is the equation of the line that passes through the points (0,35) , (−12,34) ?(1 point) Responses y=−310x+35 y is equal to negative 3 tenths x plus 3 fifths y=35x−310 y is equal to 3 fifths x minus 3 tenths y=−310x−35 y is equal to negative 3 tenths x minus 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 need to determine the slope of the line and then use the point-slope form of the equation.

1. **Calculate the slope (m)**:
The formula for the slope \(m\) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Here, \((x_1, y_1) = (0, 35)\) and \((x_2, y_2) = (-12, 34)\):
\[
m = \frac{34 - 35}{-12 - 0} = \frac{-1}{-12} = \frac{1}{12}
\]

2. **Use the point-slope form**:
The point-slope form of the equation of a line is:
\[
y - y_1 = m(x - x_1)
\]
We'll use the point \((0, 35)\):
\[
y - 35 = \frac{1}{12}(x - 0)
\]
Simplifying this gives:
\[
y - 35 = \frac{1}{12}x
\]
\[
y = \frac{1}{12}x + 35
\]

3. **Convert to slope-intercept form** (if necessary):
The equation is already in slope-intercept form \(y = mx + b\), where \(m = \frac{1}{12}\) and \(b = 35\).

None of the provided options directly match this equation. Thus, it seems that there might be a miscommunication in the options provided.

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