Algebra Class 10: Transformations and Slopes
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Questions and Answers

What effect does the transformation f(x + h) have on the graph?

  • Translates up
  • Translates down
  • Translates right
  • Translates left (correct)

Which transformation occurs when using -f(x)?

  • Reflection over x-axis (correct)
  • Vertical translation down
  • Vertical translation up
  • Reflection over y-axis

How does the slope of the function change during a dilation?

  • It remains the same
  • It becomes negative
  • It changes depending on the stretch (correct)
  • It always increases

What happens to the orientation of the graph when it is shrunk?

<p>It remains the same (D)</p> Signup and view all the answers

Which of the following transformations translates the graph 3 units down?

<p>f(x) - 3 (B)</p> Signup and view all the answers

What is the point-slope form of a line given point (-1, -1) and a slope of 1?

<p>y + 1 = 1(x + 1) (A)</p> Signup and view all the answers

Which of the following is a characteristic of parallel lines in relation to slope?

<p>They have the same slope. (A)</p> Signup and view all the answers

In the slope-intercept form, what does the variable 'b' represent?

<p>The y-intercept of the line. (D)</p> Signup and view all the answers

What is the first step to convert a linear equation from standard form to slope-intercept form?

<p>Isolate the variable 'y'. (B)</p> Signup and view all the answers

What characteristic do parallel lines share?

<p>They share the same slope. (A)</p> Signup and view all the answers

What is the slope of a line defined by the equation y = 2x - 3?

<p>2 (A)</p> Signup and view all the answers

What is true about the slopes of perpendicular lines?

<p>They are opposite reciprocals. (D)</p> Signup and view all the answers

Which equation represents a linear function where the slope is 1?

<p>y = x (D)</p> Signup and view all the answers

What describes the intersection of perpendicular lines?

<p>They intersect at a right angle. (A)</p> Signup and view all the answers

What can be said about the y-intercepts of parallel lines?

<p>They are always different. (D)</p> Signup and view all the answers

What does a positive correlation indicate about the relationship between two variables?

<p>Variables move in the same direction. (D)</p> Signup and view all the answers

Which range is indicative of a strong correlation in the R-Correlation Coefficient?

<p>-5 to -3 or 3 to 5 (A)</p> Signup and view all the answers

What is an indication of a weak correlation between two variables?

<p>Points are more spread out. (A)</p> Signup and view all the answers

If the correlation coefficient is 0, what can be inferred about the relationship between the two variables?

<p>There is no linear relationship. (B)</p> Signup and view all the answers

What is the main characteristic of a strong correlation?

<p>Points are very close to a line. (A)</p> Signup and view all the answers

What is the first step in graphing a linear inequality?

<p>Put the inequality in slope-intercept form (D)</p> Signup and view all the answers

When is a dashed line used to graph a linear inequality?

<p>When the inequality is less than or greater than (C)</p> Signup and view all the answers

What happens to the inequality sign when multiplying by a negative number?

<p>It is flipped (B)</p> Signup and view all the answers

Which direction do you shade when graphing the inequality $y < 2x + 3$?

<p>Below the line (B)</p> Signup and view all the answers

What type of line represents the inequality $x eq 5$?

<p>Dashed line (D)</p> Signup and view all the answers

Flashcards

Horizontal Translation

Shifting a graph left or right.

Vertical Translation

Shifting a graph up or down.

Dilation of a Graph

Stretching or compressing a graph.

Reflection over x-axis

Flipping a graph upside down (across the x-axis).

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Reflection over y-axis

Flipping a graph horizontally (across the y-axis).

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Point-slope form equation

y - y₁ = m(x - x₁)

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Slope formula

m = (y₂ - y₁)/(x₂ - x₁)

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Slope-intercept form

y = mx + b

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Find parallel line

Same slope, different y-intercept

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Standard form

Ax + By = C

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Parallel Lines

Lines that have the same slope and never intersect.

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Perpendicular Lines

Lines that intersect at a 90-degree angle and have slopes that are opposite reciprocals.

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Slope of Parallel Lines

Parallel lines share the same slope. This means their rate of change is identical.

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Slope of Perpendicular Lines

Perpendicular lines have slopes that are opposite reciprocals. This means one slope is the negative inverse of the other.

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Y-intercept of Parallel Lines

Parallel lines have different y-intercepts, meaning they cross the y-axis at different points.

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Positive Correlation

When one variable increases, the other tends to increase as well. The points on the scatter plot form an upward trend.

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Negative Correlation

When one variable increases, the other tends to decrease. The points on the scatter plot form a downward trend.

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Strong Correlation

The points on the scatter plot are clustered closely together forming a clear trend, either upward or downward.

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Weak Correlation

The points on the scatter plot are spread out, with no clear upward or downward trend.

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R-Correlation Coefficient

A numerical value that measures the strength and direction of a linear relationship between two variables. It ranges from -1 to 1.

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Solid line

Used in graphing linear inequalities when the inequality includes 'or equal to' (≤ or ≥). This indicates that points on the line are included in the solution set.

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Dashed line

Used in graphing linear inequalities when the inequality does not include 'or equal to' (< or >). Points on the line are not part of the solution.

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Shading above/below

Used to indicate the area where all solutions to the inequality are found. Shade above if 'y' is greater than, shade below if 'y' is less than.

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Flip the inequality sign

When multiplying or dividing both sides of an inequality by a negative number, the direction of the inequality sign must be reversed.

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