Alejandra originally wrote the equation [tex]\( y - 3 = \frac{1}{5}(x - 10) \)[/tex] to represent a line passing through the point (10, 3) with a slope of [tex]\( \frac{1}{5} \)[/tex].
Now, the teacher wants to change the line so that it has a slope of 2 but still passes through the same point (10, 3). To create the new equation, we need to use the point-slope form of a linear equation:
[tex]\[
y - y_1 = m(x - x_1)
\][/tex]
Here, [tex]\( (x_1, y_1) \)[/tex] is the point the line passes through, and [tex]\( m \)[/tex] is the slope.
Given:
- The point [tex]\( (x_1, y_1) = (10, 3) \)[/tex]
- The new slope [tex]\( m = 2 \)[/tex]
Substitute these values into the point-slope form:
[tex]\[
y - 3 = 2(x - 10)
\][/tex]
Thus, the correct new equation is:
[tex]\[
y - 3 = 2(x - 10)
\][/tex]
Therefore, the equation that Alejandra should write to represent the new line is:
[tex]\[
y - 3 = 2(x - 10)
\][/tex]
The correct choice from the given options is:
[tex]\[ y - 3 = 2(x - 10) \][/tex]
