Answer:
y = 2x + 8
Step-by-step explanation:
Using two ordered pairs from the table: (4, 16) and (8, 24):
Let (x1, y1) = (4, 16)
(x2, y2) = (8, 24)
We can start by solving for the slope of the line by using the formula:
[tex]m = \frac{y2 - y1}{x2 - x1} = \frac{24 - 16}{8 - 4} = \frac{8}{4} = 2[/tex]
Therefore, the slope of the line is 2.
Next, we must determine the y-intercept of the line. By definition, the y-intercept is the y-coordinate of the point 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 points on the given table, (4, 16), we can plug in these values into the slope-intercept form: y = mx + b
y = mx + b
16 = 2(4) + b
16 = 8 + b
Subtract 8 on both sides of the equation to solve for the y-intecept, b:
16 - 8 = 8 + b - 8
8 = b
Now that we have our slope, m = 2, and y-intercept, b = 8, we can establish our linear equation in slope-intercept form:
y = 2x + 8
