Question

writing equations
directions: write the equation of the line below the graph and then write the letter in the space above.
name: lyella gaskell
period: 4th
$y = \frac{1}{2}x - 3 \to$
$y = -\frac{3}{2}x + 1 \to$
$y = \frac{1}{3}x + 2 \to$
$y = \frac{3}{4}x - 2 \to$
$y = -3x + 4 \to$
$y = 2x - 2 \to a$
$y = -\frac{1}{2}x \to$
$y = \frac{1}{3}x - 3 \to$
$y = \frac{3}{4}x + 1 \to$

a
$m=\frac{2}{1}$ $b=-2$
$eq:y=2x-2$

b
$m=$ $b=-3$
$eq: y=$

c
$m=$ $b=0$
$eq: y=$

d
$m=$ $b=-2$
$eq: y=$

e
$m=$ $b=4$
$eq: y=$

f
$m=$ $b=1$
$eq: y=$

g
$m=$ $b=-3$
$eq: y=$

h
$m=$ $b=2$
$eq: y=$

i
$m=$ $b=1$
$eq: y=$

Explanation:

Let's solve for the equation of line B.

Step 1: Identify the slope-intercept form

The slope - intercept form of a line is \(y = mx + b\), where \(m\) is the slope and \(b\) is the y - intercept.

From the given information for line B, we know that \(b=- 3\). We need to find the slope \(m\).

Looking at the equation options, we have an equation \(y=\frac{1}{3}x - 3\) which has a y - intercept \(b = - 3\). Let's check the slope.

To find the slope from a graph, we can use the formula \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Let's assume two points on the line. If we consider the y - intercept \((0,-3)\) and another point. Let's take \(x = 3\), then for the line \(y=\frac{1}{3}x-3\), when \(x = 3\), \(y=\frac{1}{3}(3)-3=1 - 3=-2\). So two points on the line are \((0,-3)\) and \((3,-2)\).

Step 2: Calculate the slope

Using the slope formula \(m=\frac{y_2 - y_1}{x_2 - x_1}\), with \((x_1,y_1)=(0,-3)\) and \((x_2,y_2)=(3,-2)\)

\(m=\frac{-2-(-3)}{3 - 0}=\frac{-2 + 3}{3}=\frac{1}{3}\)

Step 3: Write the equation

Since \(m=\frac{1}{3}\) and \(b=-3\), the equation of the line in slope - intercept form is \(y=\frac{1}{3}x-3\)

Answer:

The equation of line B is \(y = \frac{1}{3}x-3\)