To determine the correct equation of the line with the new slope, we will follow these steps.
1. Identify the original point and the new slope:
- The original line passes through the point (10, 3) and has a new slope of 2.
2. Use the point-slope form of a line equation:
- The point-slope form is [tex]\( y - y_1 = m (x - x_1) \)[/tex], where [tex]\((x_1, y_1)\)[/tex] is a point on the line and [tex]\(m\)[/tex] is the slope.
3. Substitute the given point and slope into the point-slope form:
- Here, we have [tex]\( x_1 = 10 \)[/tex], [tex]\( y_1 = 3 \)[/tex], and [tex]\( m = 2 \)[/tex].
4. Plug these values into the point-slope equation:
[tex]\[
y - 3 = 2(x - 10)
\][/tex]
Thus, the correct equation that Alejandra should write to represent the new line is:
[tex]\[
y - 3 = 2(x - 10)
\][/tex]
Therefore, the correct answer is:
[tex]\[
\boxed{y-3=2(x-10)}
\][/tex]
