Question

40 POINTS PLS HELP PLS PLS PLS PLS PLS PLS PLS PLS PLS PLS /J IM LAZY NO PLS HELP

Answer 1

The formula of a line is:

`f(x) = kx + b`

k — stands for tg of line angle
b — stands for the y value of a point where the line crosses y axis.

We can see 2 points:
A (1, -4)
B (3, -5)

We can make a system of equations:

`k*1+b=-4\\k*3+b=-5\\`

From second equation:

`b = -5 - 3k`

Let's put b in first equation:

`k-5-3k=-4\\-2k=1\\k=- (1)/(2)`

Now we can find b:

`b = -5 -3*- (1)/(2)\\b = -5 + 1.5\\b = -3.5`

The answer is:
-0.5x -3.5

Answer 2

y = -0.5x - 3.5

Step-by-step explanation:

Take two points: (1, -4), (3, -5)

Find slope:

`\sf slope: (y_2 - y_1)/(x_2- x_1) \ \ where \ (x_1 , \ y_1), ( x_2 , \ y_2) \ are \ points`

`\rightarrow \sf slope \ (m) : (-5-(-4))/(3-1) = -(1)/(2)`

Equation:

`\sf y- y_1 = m (x - x_1)`

`\rightarrow \sf y- (-4) = -(1)/(2) (x -1)`

`\rightarrow \sf y+ 4 = -(1)/(2) x + (1)/(2)`

`\rightarrow \sf y = -(1)/(2) x + (1)/(2) - 4`

`\rightarrow \sf y = -0.5 x -3.5`