Question

identify the slope & y-intercept from each equation written in slope-intercept form (y=mx + b).

1. $y = -2x + 6$

slope (m) =
$y$-intercept (b) =

1. $y = x - 7$

slope (m) =
$y$-intercept (b) =

1. $y = 2x - \frac{5}{2}$

slope (m) =
$y$-intercept (b) =

1. $y = 3$

slope (m) =
$y$-intercept (b) =

1. $y = 4x$

slope (m) =
$y$-intercept (b) =

1. $y = -\frac{5}{9}x - \frac{3}{4}$

slope (m) =
$y$-intercept (b) =

identify the slope and the $y$-intercept. then graph each equation

1. $y = \frac{3}{4}x$

slope (m) =
$y$-intercept (b) =
\

$$\begin{tikzpicture}scale=0.5 \\draw-> (-5,0) -- (5,0) noderight {$x$}; \\draw-> (0,-5) -- (0,5) nodeabove {$y$}; \\foreach \\x in {-5,-4,-3,-2,-1,1,2,3,4,5} \\draw (\\x,0.1) -- (\\x,-0.1) nodebelow {\\x}; \\foreach \\y in {-5,-4,-3,-2,-1,1,2,3,4,5} \\draw (0.1,\\y) -- (-0.1,\\y) nodeleft {\\y}; \\end{tikzpicture}$$

1. $y = -3x + 5$

slope (m) =
$y$-intercept (b) =
\

$$\begin{tikzpicture}scale=0.5 \\draw-> (-5,0) -- (5,0) noderight {$x$}; \\draw-> (0,-5) -- (0,5) nodeabove {$y$}; \\foreach \\x in {-5,-4,-3,-2,-1,1,2,3,4,5} \\draw (\\x,0.1) -- (\\x,-0.1) nodebelow {\\x}; \\foreach \\y in {-5,-4,-3,-2,-1,1,2,3,4,5} \\draw (0.1,\\y) -- (-0.1,\\y) nodeleft {\\y}; \\end{tikzpicture}$$

1. $y = -\frac{1}{4}x - 2$

slope (m) =
$y$-intercept (b) =
\

$$\begin{tikzpicture}scale=0.5 \\draw-> (-5,0) -- (5,0) noderight {$x$}; \\draw-> (0,-5) -- (0,5) nodeabove {$y$}; \\foreach \\x in {-5,-4,-3,-2,-1,1,2,3,4,5} \\draw (\\x,0.1) -- (\\x,-0.1) nodebelow {\\x}; \\foreach \\y in {-5,-4,-3,-2,-1,1,2,3,4,5} \\draw (0.1,\\y) -- (-0.1,\\y) nodeleft {\\y}; \\end{tikzpicture}$$

Explanation:

Problem 1: \( y = -2x + 6 \)

Step1: Identify slope (m)

In \( y = mx + b \), \( m \) is the coefficient of \( x \). Here, coefficient of \( x \) is \( -2 \).
\( m = -2 \)

Step2: Identify y-intercept (b)

In \( y = mx + b \), \( b \) is the constant term. Here, constant term is \( 6 \).
\( b = 6 \)

Step1: Identify slope (m)

Rewrite \( y = x - 7 \) as \( y = 1x - 7 \). Coefficient of \( x \) is \( 1 \).
\( m = 1 \)

Step2: Identify y-intercept (b)

Constant term is \( -7 \).
\( b = -7 \)

Step1: Identify slope (m)

Coefficient of \( x \) is \( 2 \).
\( m = 2 \)

Step2: Identify y-intercept (b)

Constant term is \( -\frac{5}{2} \).
\( b = -\frac{5}{2} \)

Answer:

slope (m) = \(-2\)
y-intercept (b) = \(6\)

Problem 2: \( y = x - 7 \)