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Alejandra correctly wrote the equation [tex]\( y - 3 = \frac{1}{5}(x - 10) \)[/tex] to represent a line that her teacher sketched. The teacher then changed the line so it had a slope of 2, but still went through the same point. Which equation should Alejandra write to represent the new line?

A. [tex]\( y - 6 = 2(x - 10) \)[/tex]
B. [tex]\( y - 2 = \frac{1}{5}(x - 10) \)[/tex]
C. [tex]\( y - 3 = \frac{1}{5}(x - 2) \)[/tex]
D. [tex]\( y - 3 = 2(x - 10) \)[/tex]



Answer :

GinnyAnswer
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]

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