What are the first three terms of the Arithmetic Sequence a_n = 15 – 2(n – 1)?
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<u>Given:</u>
The equation of the line passes through the point (6,9) and is perpendicular to the line whose equation is
We need to determine the equation of the line.
<u>Slope</u>:
Let us convert the equation to slope - intercept form.
From the above equation, the slope is
Since, the lines are perpendicular, the slope of the line can be determined using the formula,
Therefore, the slope of the equation is
<u>Equation of the line:</u>
The equation of the line can be determined using the formula,
Substituting the point (6,9) and the slope in the above formula, we get;
Simplifying the terms, we get;
Thus, the equation of the line is
The slope of the function, f(x) can be determined by choosing two sets of ordered pairs from the table and substituting their values into the slope formula.
Let (x1, y1) = (0, -1)
(x2, y2) = (1, 7)
Plug these values into the slope formula:
m = (y2 - y1)/(x2 - x1)
m = [7 - (-1)] / [1 - 0]
m = (7 + 1) / 1
m = 8/1 or 8.
Therefore, the slope of f(x), m = 8.
The y-intercept of the function, f(x) is given by (0, -1), as it is the point on the graph where it crosses the y-axis. It is also the value of y when x = 0.
The equation of the linear function, f(x) is:
f(x) = 8x - 1.
Given the slope-intercept form, y = mx + b, where m represents the slope of the line, and b represents the y-intercept:
The function, g(x) = 3x - 2 has a slope of 3, and y-intercept of -2.
Comparing the slope and y-intercept of the two functions, f(x) and g(x):
The slope of f(x), m = 8 is greater and steeper than the slope of g(x), m = 3. The y-intercept of f(x), b = -1 is greater than the y-intercept of g(x), b = -2.
Attached is a screenshot of the graph of both lines, including their y-intercepts. The blue line is g(x) = 3x - 2, and the red line is f(x) = 8x - 1.
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Let (x1, y1) = (0, -1)
(x2, y2) = (1, 7)
Plug these values into the slope formula:
m = (y2 - y1)/(x2 - x1)
m = [7 - (-1)] / [1 - 0]
m = (7 + 1) / 1
m = 8/1 or 8.
Therefore, the slope of f(x), m = 8.
The y-intercept of the function, f(x) is given by (0, -1), as it is the point on the graph where it crosses the y-axis. It is also the value of y when x = 0.
The equation of the linear function, f(x) is:
f(x) = 8x - 1.
Given the slope-intercept form, y = mx + b, where m represents the slope of the line, and b represents the y-intercept:
The function, g(x) = 3x - 2 has a slope of 3, and y-intercept of -2.
Comparing the slope and y-intercept of the two functions, f(x) and g(x):
The slope of f(x), m = 8 is greater and steeper than the slope of g(x), m = 3. The y-intercept of f(x), b = -1 is greater than the y-intercept of g(x), b = -2.
Attached is a screenshot of the graph of both lines, including their y-intercepts. The blue line is g(x) = 3x - 2, and the red line is f(x) = 8x - 1.
Please mark my answers as the Brainliest if you find this helpful :)