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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]

Sagot :

GinnyAnsweridn
To determine the new equation of the line that maintains the same point but has a different slope, we can follow these steps:

1. Identify the point on the line: The original line passes through the point [tex]\((10, 3)\)[/tex].

2. Determine the new slope: The slope of the new line is given as [tex]\(2\)[/tex].

3. Use the point-slope form: The point-slope form of the equation of a line 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.

Given the point [tex]\((10, 3)\)[/tex] and the slope [tex]\(m = 2\)[/tex], we substitute these values into the point-slope form:

[tex]\[ y - 3 = 2(x - 10) \][/tex]

Therefore, the equation of the new line is:

[tex]\[ y - 3 = 2(x - 10) \][/tex]

Among the given options, the correct answer is:

[tex]\[ y - 3 = 2(x - 10) \][/tex]

So, Alejandra should write:

[tex]\[ y - 3 = 2(x - 10) \][/tex]
Heatheridn

Answer: D. y - 3 = 2(x - 10)

Step-by-step explanation:

      This equation is written in point-slope form. This form goes y - y1 = m(x-  x1), where m is the slope and (x1, y1) is a coordinate point on the graph.

      Since the graph goes through the same point, the equation will still have y = 3 = m(x - 10). Then, we will substitute the new slope for m = 2.

      This gives us answer option D, y - 3 = 2(x - 10).

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