Input 1,2,3,4,5, n output 7,9,11,13, ?please help me find the linear function!

f(x) = 2x + 5.

Step-by-step explanation:

The input values are your x-coordinates, while the output values are your y-coordinates. You could simply select two pairs of coordinates and solve for the slope, using the formula:

m = (y2 - y1)/(x2 - x1)

Let (x1, y1) = (1, 7)

(x2, y2) = (2, 9)

Substitute these values into the slope formula:

m = (y2 - y1)/(x2 - x1)

m = (9 - 7) / (2 - 1)

m = 2/1 = 2

Therefore, the slope of the line is 2.

Next, we need to determine the y-intercept. The y-coordinate (b) of the point, (0, b ) is the y-intercept of the line where the graph of the linear equation crosses the y-axis. The y-intercept is also the value of y when x = 0.

Using the slope, m = 2, and one of the given points, (1, 7), substitute these values into the slope-intercept form [f(x)= mx + b]to solve for the y-intercept, b:

f(x) = mx + b

7 = 2(1) + b

7 = 2 + b

Subtract 2 from both sides to solve for b:

7 - 2 = 2 - 2 + b

5 = b

Therefore, the y-intercept, b = 5.

Given the slope, m = 2, and the y-intercept, b = 5:

The linear function is: f(x) = 2x + 5.

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y=2x+5

Step-by-step explanation:

the line of