Questions: Find the Equation of the Parallel Line Instructions: Find the equation of the line through point (-2,3) and parallel to y=x+1. Use a forward slash (i.e. "/") for fractions (e.g. 1 / 2 for 1/2 ). y=

$Find the Equation of the Parallel Line Instructions: Find the equation of the line through point (-2,3) and parallel to y=x+1. Use a forward slash (i.e. "/") for fractions (e.g. 1 / 2 for 1/2 ). y=$

Transcript text: Find the Equation of the Parallel Line Instructions: Find the equation of the line through point $(-2,3)$ and parallel to $y=x+1$. Use a forward slash (i.e. "/") for fractions (e.g. $1 / 2$ for $\frac{1}{2}$ ). \[ y= \] Check

Solution

Solution Steps

To find the equation of a line parallel to a given line, we need to use the same slope as the given line. The given line is \( y = x + 1 \), which has a slope of 1. We then use the point-slope form of the equation of a line, \( y - y_1 = m(x - x_1) \), where \( m \) is the slope and \( (x_1, y_1) \) is the given point.

Solution Approach

Identify the slope of the given line, which is 1.
Use the point-slope form of the line equation with the point \((-2, 3)\) and the slope 1.
Simplify the equation to get it in the slope-intercept form \( y = mx + b \).

Step 1: Identify the Slope

The given line is \( y = x + 1 \). The slope \( m \) of this line is \( 1 \).

Step 2: Use the Point-Slope Form

We need to find the equation of a line that is parallel to the given line and passes through the point \( (-2, 3) \). Using the point-slope form of the equation of a line, we have: \[ y - y_1 = m(x - x_1) \] Substituting \( m = 1 \), \( x_1 = -2 \), and \( y_1 = 3 \): \[ y - 3 = 1(x + 2) \]

Step 3: Simplify the Equation

Now, we simplify the equation: \[ y - 3 = x + 2 \] Adding \( 3 \) to both sides gives: \[ y = x + 5 \]

Final Answer

The equation of the parallel line is \[ \boxed{y = x + 5} \]

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A study examined whether the content of TV shows influenced the ability of viewers to recall brand names of items featured in the commercials. Analysts recorded the number of advertised brand names a group of people recalled immediately after watching TV shows and then that same group of people recalled 24 hours later. Strangely enough, it appears that they remembered more about the ads the next day. Should we conclude this is true in general about people's memory of TV ads? Complete parts a through d. c) How might the design of this experiment have tainted these results? A. Since the populations of each group are not normally distributed, subjects with high recall could skew the means for each group. B. Since the populations of each group are not normally distributed, a two-sample t-test is not appropriate to compare the means between the two groups. C. Since the subjects were not selected at random, the first interview might have helped the subjects with high recall to remember the brand names for a longer period of time than they would have otherwise. D. A subject with high recall right after the show might have high recall 24 hours later as well. Also, the first interview might have helped the subjects to remember the brand names for a longer period of time than they would have otherwise. d) Suggest a design that could compare immediate brand name recall with recall one day later. A. Randomly assign half of the group watching violent TV shows to be interviewed immediately after watching, while the other half of the group is interviewed 24 hours later. B. Assign the older half of the group watching violent TV shows to be interviewed immediately after watching, while the younger half of the group is interviewed 24 hours later. C. Assign subjects in the group with horrible short-term memory to be interviewed immediately after watching the violent TV show, and assign subjects with horrible long-term memory to be interviewed 24 hours later. D. Assign subjects in the group with good short-term memory to be interviewed immediately after watching the violent TV show, and assign subjects with good long-term memory to be interviewed 24 hours later.

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