Given the table:
x y
-6 -4
-5 -9
-4 -14
-3 -19
-2 -24
Let's find the equation of the linear function reresented by the table shown in slope-intercept form.
Apply the slope-intercept form of a linear equation:
y = mx + b
Where m is the slo and b is the y-intercept.
To find the slope, apply the slope formula:
[tex]m=\frac{y2-y1}{x2-x2}[/tex]
Take any two points on the line:
(x1, y1) ==> (-6, -4)
(x2, y2) ==> (-5, -9)
Thus, we have:
[tex]\begin{gathered} m=\frac{-9-(-4)}{-5-(-6)} \\ \\ m=\frac{-9+4}{-5+6} \\ \\ m=\frac{-5}{1} \\ \\ m=-5 \end{gathered}[/tex]
The slope (m) = -5.
To find the y-intercept, substitite for -5 for m, then input the values of any point for x and y in (y = mx + b).
Take the point:
(x, y) ==> (-6, -4)
Hence, we have:
y = mx + b
-4 = -5(-6) + b
-4 = 30 + b
Subtract 30 from both sides:
-4 - 30 = 30 - 30 + b
-34 = b
b = -34
The y-intercept, (b) = -34.
To write the equation, subsutitute -5 for m and -34 for b in (y = mx + b)
Hence, the equation of the line is:
y = -5x - 34
ANSWER:
[tex]y=-5x-34[/tex]
