Answer:
slope = 2/5
y-intercept = (0, 14) or 14.
Step-by-step explanation:
We could use the given table of values to solve for the slope and the y-intercept of the line.
Choose two ordered pairs from the table: (5, 16) (10, 18)
Let (x1, y1) = (5, 16)
(x2, y2) = (10, 18)
Substitute these values into the following slope formula:
m = (y2 - y1)/(x2 - x1)
m = (18 - 16)/(10 - 5)
m = 2/5
Therefore, the slope of the line is 2/5.
The y-intercept is the y-coordinate of the point (0, b ) where the graph crosses the y-axis. The y-intercept is also the value of y when x = 0.
To find the y-intercept, we'll use the slope and one of the given ordered pairs (points) from the table (5, 16). Substitute these values into the slope-intercept form, y = mx + b, where m = slope, and b = y-intercept.
y = mx + b
16 = 2/5(5) + b
16 = 2 + b
Subtract 2 from both sides to isolate b:
16 - 2 = 2 - 2 + b
14 = b
The value of the y-intercept = 14 [this is the y-coordinate of the y-intercept, (0, 14)].
Therefore, the equation of the line is: y = 2/5x + 14.
