Answer/Step-by-step explanation:
7. ✍️First Equation:
To generate the equation of the gray, which will be in the slope-intercept form, y = mx + b, we need to find the slope of the graph, m, and the y-intercept, b.
Using two points on the line, (2, 4) and (4, 0),
[tex] slope (m) = \frac{y_2 - y_1}{x_2 - x_1} = \frac{0 - 4}{4 - 2} = \frac{-4}{2} = -2 [/tex]
Substitute x = 2, y = 4 and m = -2 into y = mx + b, to find the value of b.
thus:
4 = (-2)(2) + b
4 = -4 + b
Add 4 to both sides
4 + 4 = b
b = 8
Substitute m = -2 and b = 8 into y = mx + b.
The first equation would be:
✅ y = -2x + 8
✍️Second Equation:
Using two points on the line, (1, 6) and (5, -2),
[tex] slope (m) = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-2 - 6}{5 - 1} = \frac{-6}{4} = -\frac{3}{2} [/tex]
Substitute x = 1, y = 6 and m = -³/2 into y = mx + b, to find the value of b.
thus:
6 = (-³/2)(1) + b
6 = -³/2 + b
Add ³/2 to both sides
6 + ³/2 = b
(12 + 3)/2 = b
15/2 = b
Substitute m = -³/2 and b = 15/2 into y = mx + b.
The second equation would be:
✅ [tex] y = -\frac{3}{2}x + \frac{15}{2} [/tex]
