Writing an Equation of a Line in Slope-Intercept Form given the Table of Values
Answer:
[tex]y = -2x -2[/tex]
Step-by-step explanation:
Please refer to my Answer from this Question to know about Slope-Intercept Forms:
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In writing the equation in its Slope-Intercept Form, we must first find the slope of the line. We can choose the points [tex](1, -4)[/tex] and [tex](2,-6)[/tex].
Solving for the slope:
[tex]m = \frac{y_2 -y_1}{x_2 -x_1} \\ m = \frac{-6 -(-4)}{2 -1} \\ m = \frac{-6 +4}{2 -1} \\ m = \frac{-2}{1} \\ m = -2[/tex]
The equation of a line written in Slope-Intercept Form is [tex]y = mx +b[/tex]. Now we know what [tex]m[/tex] is, all we need to do now is to find [tex]b[/tex]. Luckily for us, we are given a bunch of points in the given Table of Values. We can choose [tex](3, -8)[/tex] but you can choose any point shown in the Table of Values.
Solving for [tex]b[/tex]:
[tex]y = mx +b \\ -8 = (-2)(3) +b \\ -8 = -6 +b \\ -8 +6 = -6 +b +6 \\ -2 = b[/tex]
Now we know what [tex]b[/tex] and [tex]m[/tex] are. We can finally write the equation of a line in Slope-Intercept Form.
The equation is [tex]y = -2x -2[/tex].
