Question

hello please help me with my homework ! I would really appreciate it! :)))

Answer 1

At graph of Number 4: Let's first determine the equation of each line.

LINE 1: Let's use point A: (x1,y1) = (-5,-5) and point B: (x2,y2) = (-3,-4).

Getting the slope (m):

$\text{ m = }\frac{y_2-y_1_{}}{x_2-x_1}$$\text{ m = }\frac{-4\text{ - (-5)}}{-3\text{ - (-5)}}\text{ = }\frac{-4\text{ + 5}}{-3\text{ + 5}}\text{ = }\frac{1}{2}$

Getting the y-intercept (b): Use m = 1/2 and x,y = -5,-5

$\text{ y = mx + b}$$-5\text{ = (}\frac{1}{2})(-5)\text{ + b}$$\text{ -5 = }\frac{-5}{2}\text{ + b }\rightarrow\text{ b = -5 + }\frac{5}{2}$$\text{b = }\frac{\text{-10}}{2}\text{ + }\frac{5}{2}\text{ = }\frac{-10\text{ + 5}}{2}$$\text{ b = -}\frac{5}{2}$

Let's complete the equation: Substitute m and b in y = mx + b.

$\text{ y = mx + b}$$\text{ y = (}\frac{1}{2})x\text{ + (-}\frac{5}{2})$$\text{ y = }\frac{1}{2}x\text{ - }\frac{5}{2}\text{ ; f(x) = }\frac{1}{2}x\text{ - }\frac{5}{2}$

LINE 2: Let's use point A: (x1,y1) = (-3,-2) and point B: (x2,y2) = (1,0).

Getting the slope (m):

$\text{ m = }\frac{y_2-y_1}{x_2-x_1}$$\text{ m = }\frac{0-(-2)}{1-(-3)}=\frac{0\text{ + 2}}{1\text{ + 3}}\text{ = }\frac{2}{4}\text{ = }\frac{1}{2}$

Getting the y-intercept (b): Use m = 1/2 and x,y = 1,0

$\text{ y = mx + b}$$\text{ 0 = (}\frac{1}{2})(1)\text{ + b}$$\text{ 0 = }\frac{1}{2}\text{ + b}$$\text{ b = -}\frac{1}{2}$

Let's complete the equation: Substitute m and b in y = mx + b.

$\text{ y = mx + b}$$\text{ y = (}\frac{1}{2})x\text{ + }(-\frac{1}{2})$$\text{ y = }\frac{1}{2}x\text{ - }\frac{1}{2}\text{ ; f(x) = }\frac{1}{2}x\text{ - }\frac{1}{2}$

LINE 3: Let's use point A: (x1,y1) = (1,2) and point B: (x2,y2) = (3,3).

Getting the slope (m):

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