Answer:
[tex] y = 3x + 2 [/tex]
Step-by-step explanation:
The equation of a linear function in slope-intercept form is: y = mx + b, where, m = slope, and b = y-intercept.
Find slope (m) of the linear function by using any two points, say (3, 11) and (7, 23):
[tex] m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{23 - 11}{7 - 3} = \frac{12}{4} = 3 [/tex]
To find the y-intercept (b), substitute the value of the corrdinate pair of any of the points represented on the table, and the value of the slope (m) into [tex] y = mx + b [/tex].
Substituting, x = -1, y = -1, m = 3.
[tex] y = mx + b [/tex]
[tex] -1 = 3(-1) + b [/tex]
[tex] -1 = -3 + b [/tex]
Add 3 to both sides
[tex] -1 + 3 = b [/tex]
[tex] 2 = b [/tex]
[tex] b = 2 [/tex]
Substitute m = 3, and b = 2 into the equation of the linear function in slope-intercept form:
[tex] y = mx + b [/tex]
[tex] y = 3x + 2 [/tex]
