Question

10 choose the 3 forms of the equation that match the graph below.

a \\((y - 2) = -3(x - 1)\\)
b \\(y = -3x + 5\\)
c \\((y + 2) = -\frac{1}{3}(x + 6)\\)
d \\(y = -\frac{1}{3}x + \frac{1}{2}\\)
e \\(3x + y = 5\\)
f \\(x - 3y = -\frac{1}{2}\\)

Explanation:

⚡ Using what you learned: graphing linear equations

Step 1: Find the slope and y-intercept

Identify two points on the line from the graph:

• \( (0, 5) \)
• \( (1, 2) \)

Calculate the slope \( m \):

$$ m = \frac{2 - 5}{1 - 0} = -3 $$

The y-intercept \( b \) is \( 5 \).

Step 2: Write in slope-intercept form

Using \( y = mx + b \):

$$ y = -3x + 5 $$

This matches option B.

Step 3: Write in standard form

Rearrange the slope-intercept equation:

$$ 3x + y = 5 $$

This matches option E.

Step 4: Write in point-slope form

Using the point \( (1, 2) \) and slope \( m = -3 \):

$$ y - y_1 = m(x - x_1) $$

$$ y - 2 = -3(x - 1) $$

This matches option A.

Answer:

The 3 correct forms of the equation are:

• A \( (y - 2) = -3(x - 1) \)
• B \( y = -3x + 5 \)
• E \( 3x + y = 5 \)