Answer:
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.
Please mark my answers as the Brainliest, if you find this helpful :)
