Answer:
Step-by-step explanation:
For these problems involving a straight line, all you need is two points and you can describe the line
#1 the two points are (3, 3) and (-3, -1)
we can use
and
to describe the line
![m = \frac{3-(-1)}{3-(-3)} = \frac{4}{6} = \frac{2}{3} \\y = \frac{2}{3}(x) +b\\ 3 = 2*(3)/3 + b\\3 = 2 + b\\b = 1\\y = \frac{2}{3}(x)+1](https://tex.z-dn.net/?f=m%20%3D%20%5Cfrac%7B3-%28-1%29%7D%7B3-%28-3%29%7D%20%3D%20%5Cfrac%7B4%7D%7B6%7D%20%3D%20%5Cfrac%7B2%7D%7B3%7D%20%20%5C%5Cy%20%3D%20%5Cfrac%7B2%7D%7B3%7D%28x%29%20%2Bb%5C%5C%203%20%3D%202%2A%283%29%2F3%20%2B%20b%5C%5C3%20%3D%202%20%2B%20b%5C%5Cb%20%3D%201%5C%5Cy%20%3D%20%5Cfrac%7B2%7D%7B3%7D%28x%29%2B1)
#2 same process. The two points given are (-2, 1) and (2, -2)
![m = \frac{1-(-2)}{-2-2} = \frac{3}{-4} = \frac{-3}{4} \\y = \frac{-3}{4}(x) + b\\1 = \frac{-3}{4}(-2) + b\\ 1 = 1.5 + b\\b = -\frac{1}{2} \\y = \frac{-3}{4}(x) - \frac{1}{2}](https://tex.z-dn.net/?f=m%20%3D%20%5Cfrac%7B1-%28-2%29%7D%7B-2-2%7D%20%3D%20%5Cfrac%7B3%7D%7B-4%7D%20%20%3D%20%5Cfrac%7B-3%7D%7B4%7D%20%5C%5Cy%20%3D%20%5Cfrac%7B-3%7D%7B4%7D%28x%29%20%2B%20b%5C%5C1%20%3D%20%5Cfrac%7B-3%7D%7B4%7D%28-2%29%20%2B%20b%5C%5C%201%20%3D%201.5%20%2B%20b%5C%5Cb%20%3D%20-%5Cfrac%7B1%7D%7B2%7D%20%5C%5Cy%20%3D%20%5Cfrac%7B-3%7D%7B4%7D%28x%29%20-%20%5Cfrac%7B1%7D%7B2%7D)
#3 same process, (-4, 2) and (-1, -4)
![m = \frac{2+4}{-4+1} = \frac{6}{-3} = -2\\ y = -2x + b\\2 = -2(-4) + b\\2 = 8 + b\\b = -6\\y = -2x - 6](https://tex.z-dn.net/?f=m%20%3D%20%5Cfrac%7B2%2B4%7D%7B-4%2B1%7D%20%3D%20%5Cfrac%7B6%7D%7B-3%7D%20%3D%20-2%5C%5C%20%20y%20%3D%20-2x%20%2B%20b%5C%5C2%20%3D%20-2%28-4%29%20%2B%20b%5C%5C2%20%3D%208%20%2B%20b%5C%5Cb%20%3D%20-6%5C%5Cy%20%3D%20-2x%20-%206)
#4 this is a vertical line. If the <em>m</em> were to be calculated, it would be division by 0. These lines can be described by x = n, where n is any real number. In this case, x = 3
#5 same process as earlier (2, -1) and (3, 3)
![m = \frac{4}{1 } = 4\\ y = 4x + b\\3 = 12 + b\\b = -9\\y = 4x - 9](https://tex.z-dn.net/?f=m%20%3D%20%5Cfrac%7B4%7D%7B1%20%7D%20%3D%204%5C%5C%20y%20%3D%204x%20%2B%20b%5C%5C3%20%3D%2012%20%2B%20b%5C%5Cb%20%3D%20-9%5C%5Cy%20%3D%204x%20-%209)
#6 unlike #4, this is a horizontal line, meaning the slope is zero. No matter what x value, you will always get the same number. In this case, the line is
y = -2