Question

period
7)
$\

$$\begin{array}{|c|c|}\\hline x & y \\\\\\hline -4 & 3 \\\\\\hline 3 & -2 \\\\\\hline\\end{array}$$

$
$m:$_______
$b:$_______
equation:_________
8)
$\

$$\begin{array}{|c|c|}\\hline x & y \\\\\\hline 1 & 3 \\\\\\hline -2 & 0 \\\\\\hline\\end{array}$$

$
$m:$_______
$b:$_______
equation:_________
9)
$\

$$\begin{array}{|c|c|}\\hline x & y \\\\\\hline -3 & 3 \\\\\\hline -4 & -4 \\\\\\hline\\end{array}$$

$
$m:$_______
$b:$_______
equation:_________
10)
$\

$$\begin{array}{|c|c|}\\hline x & y \\\\\\hline 1 & 4 \\\\\\hline 0 & 0 \\\\\\hline\\end{array}$$

$
$m:$_______
$b:$_______
equation:_________
11)
$\

$$\begin{array}{|c|c|}\\hline x & y \\\\\\hline -4 & -1 \\\\\\hline -1 & -1 \\\\\\hline\\end{array}$$

$
$m:$_______
$b:$_______
equation:_________
12)
$\

$$\begin{array}{|c|c|}\\hline x & y \\\\\\hline -3 & 5 \\\\\\hline 4 & 3 \\\\\\hline\\end{array}$$

$
$m:$_______
$b:$_______
equation:_________

Explanation:

Problem 7

Step1: Calculate slope $m$

Use slope formula $m=\frac{y_2-y_1}{x_2-x_1}$ with $(-4,3)$ and $(3,-2)$:
$m=\frac{-2-3}{3-(-4)}=\frac{-5}{7}=-\frac{5}{7}$

Step2: Find y-intercept $b$

Substitute $(-4,3)$ and $m$ into $y=mx+b$:
$3 = -\frac{5}{7}(-4)+b \implies 3=\frac{20}{7}+b \implies b=3-\frac{20}{7}=\frac{21-20}{7}=\frac{1}{7}$

Step3: Write equation

$y=-\frac{5}{7}x+\frac{1}{7}$

Problem 8

Step1: Calculate slope $m$

Use slope formula with $(-2,0)$ and $(1,3)$:
$m=\frac{3-0}{1-(-2)}=\frac{3}{3}=1$

Step2: Find y-intercept $b$

Substitute $(-2,0)$ and $m$ into $y=mx+b$:
$0=1(-2)+b \implies b=2$

Step3: Write equation

$y=x+2$

Problem 9

Step1: Calculate slope $m$

Use slope formula with $(-3,3)$ and $(-4,-4)$:
$m=\frac{-4-3}{-4-(-3)}=\frac{-7}{-1}=7$

Step2: Find y-intercept $b$

Substitute $(-3,3)$ and $m$ into $y=mx+b$:
$3=7(-3)+b \implies 3=-21+b \implies b=24$

Step3: Write equation

$y=7x+24$

Problem 10

Step1: Calculate slope $m$

Use slope formula with $(0,0)$ and $(1,4)$:
$m=\frac{4-0}{1-0}=4$

Step2: Find y-intercept $b$

Line passes through $(0,0)$, so $b=0$

Step3: Write equation

$y=4x$

Problem 11

Step1: Calculate slope $m$

Use slope formula with $(-4,-1)$ and $(4,-1)$:
$m=\frac{-1-(-1)}{4-(-4)}=\frac{0}{8}=0$

Step2: Find y-intercept $b$

Line is horizontal, $y=-1$, so $b=-1$

Step3: Write equation

$y=-1$

Problem 12

Step1: Calculate slope $m$

Use slope formula with $(-3,5)$ and $(4,3)$:
$m=\frac{3-5}{4-(-3)}=\frac{-2}{7}=-\frac{2}{7}$

Step2: Find y-intercept $b$

Substitute $(-3,5)$ and $m$ into $y=mx+b$:
$5=-\frac{2}{7}(-3)+b \implies 5=\frac{6}{7}+b \implies b=5-\frac{6}{7}=\frac{35-6}{7}=\frac{29}{7}$

Step3: Write equation

$y=-\frac{2}{7}x+\frac{29}{7}$

Answer:

Problem 7

$m=-\frac{5}{7}$, $b=\frac{1}{7}$, Equation: $y=-\frac{5}{7}x+\frac{1}{7}$

Problem 8

$m=1$, $b=2$, Equation: $y=x+2$

Problem 9

$m=7$, $b=24$, Equation: $y=7x+24$

Problem 10

$m=4$, $b=0$, Equation: $y=4x$

Problem 11

$m=0$, $b=-1$, Equation: $y=-1$

Problem 12

$m=-\frac{2}{7}$, $b=\frac{29}{7}$, Equation: $y=-\frac{2}{7}x+\frac{29}{7}$