Answer:
y = 5/3x + 1
y-intercept: (0, 1)
Step-by-step explanation:
In order to determine the linear equation in its slope-intercept form, y = mx + b, where m = slope, b = y-intercept:
You need two ordered pairs from the table to solve for the slope:
We'll use (6, 11) and (9, 16).
Let (x1, y1) = (6, 11)
(x2, y2) = (9, 16)
Substitute thes values into the slope formula:
m = (y2 - y1)/(x2 - x1)
m = (16 - 11) / (9 - 6)
m = 5 / 3
Therefore, the slope of the line is: m = 5/3.
Next, we need to determine the y-intercept of the line. The y-intercept is the y-coordinate of the point (0, b ) where the graph of the linear equation 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, m = 5/3, and one of the ordered pairs from the table, (6, 11). Substitute these values into y = mx + b to solve for the y-intercept, (b ):
y = mx + b
11 = 5/3(6) + b
11 = 10 + b
Subtract 10 from both sides to solve for b:
11 - 10 = 10 - 10 + b
1 = b
The y-coordinate of the y-intercept, (0, b) is 1. The y-intercept as an ordered pair is (0, 1). For the linear equation in slope-intercept form, you'll use b = 1 to write the equation.
Therefore, given the slope, m = 5/3, and the y-intercept, b = 1:
The slope-intercept form is: y = 5/3x + 1
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