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) = (y_2 - y_1)/(x_2 - x_1) = (0 - 4)/(4 - 2) = (-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) = (y_2 - y_1)/(x_2 - x_1) = (-2 - 6)/(5 - 1) = (-6)/(4) = -(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 = -(3)/(2)x + (15)/(2)`