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Sagot :
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]
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]
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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