The given equation, 4x + y = 9, represents a linear function.
A linear function is a function of the form y = mx + b, where m is the slope of the line and b is the y-intercept. The slope represents the rate at which the output value (y) changes with respect to the input value (x). The y-intercept is the point where the line crosses the y-axis.
In this case, the slope of the line is 4 and the y-intercept is 9. We can use this information to plot the graph of the linear function and to find the value of y for any given value of x.
For example, if x = 2, then y = 4(2) + 9 = 8 + 9 = 17. If x = -1, then y = 4(-1) + 9 = -4 + 9 = 5.
We can also use the given equation to find the x-intercept, which is the point where the line crosses the x-axis. To find the x-intercept, we can set y equal to 0 and solve for x.
In this case, if y = 0, then 4x + y = 9 becomes 4x = 9, and x = 9/4 = 2.25.
Therefore, the x-intercept of the linear function is (2.25, 0).
Overall, the given equation, 4x + y = 9, represents a linear function with a slope of 4 and y-intercept of 9, and its graph passes through the point (2.25, 0).
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Answer:
The given equation, 4x + y = 9, represents a linear function.
A linear function is a function of the form y = mx + b, where m is the slope of the line and b is the y-intercept. The slope represents the rate at which the output value (y) changes with respect to the input value (x). The y-intercept is the point where the line crosses the y-axis.
In this case, the slope of the line is 4 and the y-intercept is 9. We can use this information to plot the graph of the linear function and to find the value of y for any given value of x.
For example, if x = 2, then y = 4(2) + 9 = 8 + 9 = 17. If x = -1, then y = 4(-1) + 9 = -4 + 9 = 5.
We can also use the given equation to find the x-intercept, which is the point where the line crosses the x-axis. To find the x-intercept, we can set y equal to 0 and solve for x.
In this case, if y = 0, then 4x + y = 9 becomes 4x = 9, and x = 9/4 = 2.25.
Therefore, the x-intercept of the linear function is (2.25, 0).
Overall, the given equation, 4x + y = 9, represents a linear function with a slope of 4 and y-intercept of 9, and its graph passes through the point (2.25, 0).