Question

I need help for this question pllsssss

Answer 1

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),

$slope (m) = \frac{y_2 - y_1}{x_2 - x_1} = \frac{0 - 4}{4 - 2} = \frac{-4}{2} = -2$

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),

$slope (m) = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-2 - 6}{5 - 1} = \frac{-6}{4} = -\frac{3}{2}$

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:

✅ $y = -\frac{3}{2}x + \frac{15}{2}$