Answer:
We conclude that the equation of the line is:
Step-by-step explanation:
The slope-intercept form of the line equation
[tex]y = mx+b[/tex]
where
Given the data table
x -3 -5 -7 -9 -11
y -16 -26 -36 -46 -56
From the table taking two points
Determining the slope between (-3, -16) and (-5, -26)
[tex]\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]\left(x_1,\:y_1\right)=\left(-3,\:-16\right),\:\left(x_2,\:y_2\right)=\left(-5,\:-26\right)[/tex]
[tex]m=\frac{-26-\left(-16\right)}{-5-\left(-3\right)}[/tex]
[tex]m=5[/tex]
Thus, the slope of the line is: m = 5
substituting m = 5 and (-3, -16) in the slope-intercept form of the line equation to determine the y-intercept b
[tex]y = mx+b[/tex]
-16 = 5(-3) + b
-16 = -15 + b
b = -16+15
b = 1
Thus, the y-intercept b = 1
now substituting m = 5 and b = 1 in the slope-intercept form of the line equation
[tex]y = mx+b[/tex]
[tex]y = 5x + 1[/tex]
Therefore, we conclude that the equation of the line is:
