Question

1. graph

the line
$y = x - 2$

1. which equation

matches the linear tab
a. $y = 1/6x + 13$
b. $y = 6x + 7$
c...
d...

x	y
1	13
2	19
3	25

Explanation:

Problem 2: Graph the line \( y = x - 2 \)

Step 1: Identify the slope and y-intercept

The equation is in slope - intercept form \( y=mx + b \), where \( m \) is the slope and \( b \) is the y - intercept. For \( y=x - 2 \), the slope \( m = 1 \) and the y - intercept \( b=-2 \).

Step 2: Plot the y - intercept

The y - intercept is \( - 2 \), so we plot the point \( (0,-2) \) on the coordinate plane.

Step 3: Use the slope to find another point

The slope \( m = 1=\frac{1}{1} \), which means for every 1 unit we move to the right (increase in \( x \) by 1), we move up 1 unit (increase in \( y \) by 1). From \( (0,-2) \), moving 1 unit right and 1 unit up gives us the point \( (1,-1) \). We can also move 1 unit left and 1 unit down from \( (0,-2) \) to get \( (-1,-3) \).

Step 4: Draw the line

Connect the points \( (0,-2) \), \( (1,-1) \), \( (-1,-3) \) (or other points found using the slope) with a straight line.

Problem 4: Which equation matches the linear table?

The table has the following values: when \( x = 0 \), \( y = 7 \); when \( x = 1 \), \( y = 13 \); when \( x = 2 \), \( y = 19 \); when \( x = 3 \), \( y = 25 \)

Step 1: Find the slope (\( m \))

The slope \( m=\frac{y_2 - y_1}{x_2 - x_1} \). Using the points \( (0,7) \) and \( (1,13) \), \( m=\frac{13 - 7}{1 - 0}=\frac{6}{1}=6 \)

Step 2: Find the y - intercept (\( b \))

The y - intercept is the value of \( y \) when \( x = 0 \). From the table, when \( x = 0 \), \( y = 7 \), so \( b = 7 \)

Step 3: Write the equation

Using the slope - intercept form \( y=mx + b \), with \( m = 6 \) and \( b = 7 \), the equation is \( y=6x + 7 \)
We can also check by substituting the values of \( x \) into the equations:

• For option A: \( y=\frac{1}{6}x + 13 \). When \( x = 0 \), \( y = 13

eq7 \), so A is incorrect.

• For option B: \( y = 6x+7 \). When \( x = 0 \), \( y=7 \); when \( x = 1 \), \( y=6\times1 + 7=13 \); when \( x = 2 \), \( y=6\times2+7 = 19 \); when \( x = 3 \), \( y=6\times3 + 7=25 \). It matches all the values in the table.
• (Assuming option C and D are incorrect based on the check, but since they are not fully visible, the correct one from the visible option is B)

Answer:

s:

• For problem 2: The line \( y = x - 2 \) is graphed by plotting \( (0,-2) \) and using the slope \( 1 \) to find other points and drawing a line through them.
• For problem 4: B. \( y = 6x + 7 \)