Algebra Class - Trends and Slopes

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What is the equation of the trend line based on the provided data?

y = 25x + 100
y = 50x + 65 (correct)
y = 60x + 50
y = 75x + 40

How much weight is estimated for an age of 3 weeks based on the trend line?

205 lbs (correct)
155 lbs
220 lbs
195 lbs

What is the change in weight from age 1 to age 5?

150 lbs
200 lbs (correct)
250 lbs
100 lbs

Which of the following calculations corresponds to finding the slope of the trend line?

200 / 4 = 50 (B) Signup and view all the answers

What is the estimated weight for an age of 6 weeks based on the trend line calculations?

370 lbs (B) Signup and view all the answers

What is the slope of a line parallel to the line given by the equation $y = 5x$?

5 (D) Signup and view all the answers

Using point-slope form, what is the equation of the line parallel to $y = 5x$ that passes through the point (3,7)?

$y - 7 = 5(x - 3)$ (A) Signup and view all the answers

If two lines are perpendicular, what is the relationship between their slopes?

The product of the slopes equals $-1$. (B) Signup and view all the answers

In the triangle formed by two intersecting perpendicular lines of lengths 3, 5, and 3, what type of triangle is represented?

Isosceles (A) Signup and view all the answers

Which of the following statements is true for a line parallel to $y = 5x$?

It can intersect $y$ at any point. (B) Signup and view all the answers

What is the first step to convert the equation `6x + 4y = 8` into slope-intercept form?

Subtract 6x from both sides (C) Signup and view all the answers

In the equation `3y - 6x = 24`, what is the value of the slope after converting to slope-intercept form?

2 (D) Signup and view all the answers

When converting the equation `5y + 25x = 25`, what is the simplified form of the equation in slope-intercept form?

y = -5x + 5 (A) Signup and view all the answers

What change occurs to the sign of the 'x' term when converting from standard form to slope-intercept form?

It changes to a positive (B) Signup and view all the answers

After converting `6x + 4y = 8` into slope-intercept form, what is the intercept (b value) on the y-axis?

2 (C) Signup and view all the answers

What is the correct representation of the x-intercept of a linear equation?

(x,0) (B) Signup and view all the answers

In the standard form $Ax + By = C$, which variables represent the coefficients?

A and B only (D) Signup and view all the answers

How are the y-intercepts derived from the standard form?

Set x = 0 in the equation Ax + By = C (A) Signup and view all the answers

What are the coordinates of the x-intercept if the equation is rewritten in standard form as $2x + 3y = 6$?

(3,0) (A) Signup and view all the answers

Given the equation $4x + 5y = 20$, what is the y-intercept?

(0,16/5) (B) Signup and view all the answers

What is the first step taken to convert the equation $3y = -\frac{2}{3}x + 8.3$ into standard form?

$48y = 16\frac{2}{3}x + 48$ (A) Signup and view all the answers

In the equation $-21x + 48y = -22$, what would be achieved by adding $21x$ to both sides?

$48y = 21x - 22$ (A) Signup and view all the answers

What is the final standard form of the equation derived from $2x + 3y = 24$?

$-3x + y = 10$ (D) Signup and view all the answers

After which step does the equation $y - 3x = 10$ convert to $3y = -3x + 10$?

After adding $3x$ to both sides (D) Signup and view all the answers

Which operation is NOT performed during the conversion of $3y = -\frac{2}{3}x + 8.3$ to standard form?

Dividing the equation (D) Signup and view all the answers

What does the variable 'h' represent in the equation $f(x) = m(x - h) + k$?

Horizontal shift (C) Signup and view all the answers

In the function $f(x) = a(x - h)2 + k$, what effect does 'k' have?

It shifts the graph vertically (B) Signup and view all the answers

If the linear function is defined as $f(x) = mx + b$, which equation represents a horizontal shift to the right by 3 units?

$f(x) = m(x - 3) + b$ (B) Signup and view all the answers

To find the y-value when given $x = -3$ in the function $f(x) = mx + b$, what is the correct step?

Insert $-3$ into the function and solve for $f(-3)$ (D) Signup and view all the answers

What is the first step to graph the function after applying a transformation?

Identify any shifts in the function (A) Signup and view all the answers

What is the slope of the line represented by Graph 1?

$rac{3}{5}$ (B) Signup and view all the answers

Which of the following equations represents Graph 2?

$y = 3x + 15$ (B) Signup and view all the answers

What is the y-intercept of the line represented by Graph 1?

3 (D) Signup and view all the answers

Which points does the line in Graph 2 pass through?

(0, 15) and (5, 30) (C) Signup and view all the answers

How would you express the slope of Graph 2 in its simplest form?

3 (A) Signup and view all the answers

What is the slope ( extit{m}) in the equation $y = -rac{1}{3}x + rac{10}{3}$ derived from point-slope form?

$-rac{1}{3}$ (C) Signup and view all the answers

In the conversion of point-slope form to slope-intercept form, what does the term $b$ represent?

The y-intercept (C) Signup and view all the answers

Which of the following represents a correct slope-intercept form derived from the point-slope form $y - 12 = 3(x + rac{5}{2})$?

$y = 3x + 10$ (A) Signup and view all the answers

What would be the final equation in slope-intercept form if $y - 5 = -3(x + 3)$ is converted?

$y = -3x + 8$ (D) Signup and view all the answers

In the equation $y - 5 = m(x - rac{1}{-3}) - 2$, if $m = -3$, what is the final slope-intercept form?

$y = -3x + 3$ (C) Signup and view all the answers

What is the slope of the line connecting the points (-8, 5) and (10, 15)?

$rac{5}{9}$ (A) Signup and view all the answers

What is the change in y-values between the points (-6, -14) and (18, -20)?

-6 (B) Signup and view all the answers

What is the slope of the line connecting the points (-6, -14) and (18, -20)?

-0.25 (D) Signup and view all the answers

Which of the following statements about slope is true based on the examples provided?

Slope can be negative or positive. (C) Signup and view all the answers

How is the slope calculated using the points (10, 15) and (-8, 5)?

$rac{15 - 5}{10 - (-8)}$ (D) Signup and view all the answers

What is the slope of the line that passes through the points (1, 2) and (3, 5)?

3/2 (B) Signup and view all the answers

Which of the following correctly describes the slope calculated from the points (1, 2) and (3, 5)?

The slope indicates a steep incline. (C) Signup and view all the answers

If the line represented in the graph was to increase more steeply between the same x-values, which of the following could be the new slope?

5/2 (A) Signup and view all the answers

In slope-intercept form, if the line with a slope of 3/2 passes through the point (1, 2), what is the y-intercept?

-1 (C) Signup and view all the answers

What does the phrase 'rise over run' refer to in the context of slope?

The vertical change divided by the horizontal change. (D) Signup and view all the answers

Trend Line

A line that represents the general direction of a set of data points on a graph.

Equation of a Trend Line

A mathematical formula that describes the relationship between variables, typically in the form 'y = mx + c', where 'm' is the slope and 'c' is the y-intercept.

Slope of a Trend Line

Represents the rate of change of the dependent variable (y) with respect to the independent variable (x). It tells us how much 'y' changes for every unit change in 'x'.

What does this equation tell us?

The equation 'y = 50x + 65' describes the relationship between age (x, in weeks) and weight (y, in lbs). It means weight increases by 50 lbs for every week older.