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slope
| Question | Answer |
|---|---|
| What is the slope-intercept form of a linear equation? | The slope-intercept form is $y = mx + b$. |
| "In the slope-intercept form $y = mx + b$, what does the variable 'm' represent?" | The variable 'm' represents the slope of the line. |
| "In the slope-intercept form $y = mx + b$, what does the variable 'b' represent?" | The variable 'b' represents the y-intercept of the line. |
| What is the standard form of a linear equation? | The standard form is $Ax + By = C$. |
| What is the point-slope form of a linear equation? | The point-slope form is $y - y_1 = m(x - x_1)$. |
| "In the point-slope form $y - y_1 = m(x - x_1)$, what does 'm' represent?" | The variable 'm' represents the slope of the line. |
| "In the point-slope form $y - y_1 = m(x - x_1)$, what does the pair $(x_1, y_1)$ represent?" | "The pair $(x_1, y_1)$ represents a specific point that the line passes through." |
| How is the slope of a line defined in terms of 'rise' and 'run'? | Slope is defined as the rise divided by the run. |
| "What is the formula for calculating the slope of a line given two points, $(x_1, y_1)$ and $(x_2, y_2)$?" | The formula for slope is $m = \frac{y_2 - y_1}{x_2 - x_1}$. |
| What does a positive slope indicate about the direction of a line on a graph? | A positive slope indicates that the line is increasing or going up from left to right. |
| What does a negative slope indicate about the direction of a line on a graph? | A negative slope indicates that the line is decreasing or going down from left to right. |
| What is the slope of any horizontal line? | The slope of a horizontal line is 0. |
| What is the slope of any vertical line? | The slope of a vertical line is undefined. |
| What is an x-intercept? | "An x-intercept is the point where the graph of an equation crosses the x-axis, and where the y-value is zero." |
| What is a y-intercept? | "A y-intercept is the point where the graph of an equation crosses the y-axis, and where the x-value is zero." |
| "To algebraically find the x-intercept of an equation, what value do you substitute for 'y'?" | You substitute 0 for the variable 'y'. |
| "To algebraically find the y-intercept of an equation, what value do you substitute for 'x'?" | You substitute 0 for the variable 'x'. |
| How are the slopes of two parallel lines related? | Parallel lines have the same slope ($m_1 = m_2$). |
| How are the slopes of two perpendicular lines related? | The slopes of perpendicular lines are negative reciprocals of each other ($m_1 = -\frac{1}{m_2}$). |
| "If the slope of a line is 2, what is the slope of a line parallel to it?" | The slope of the parallel line is also 2. |
| "If the slope of a line is $\frac{3}{4}$, what is the slope of a line perpendicular to it?" | The slope of the perpendicular line is $-\frac{4}{3}$. |
| Identify the slope (m) and y-intercept (b) in the equation $y = 3x - 5$. | The slope is $m=3$ and the y-intercept is $b=-5$. |
| Identify the slope (m) and y-intercept (b) in the equation $y = -\frac{1}{2}x + 7$. | The slope is $m=-\frac{1}{2}$ and the y-intercept is $b=7$. |
| What is the slope (m) of the line represented by the equation $y = -2$? | "The slope is $m=0$, as it represents a horizontal line." |
| "What is the primary method for graphing an equation in standard form, such as $2x + 5y = 10$?" | The primary method is to find the x- and y-intercepts and connect them. |
| "Given the equation $y - 1 = 4(x - 5)$, identify the slope and a point on the line." | "The slope is $m=4$ and a point on the line is $(5, 1)$." |
| "Given the equation $y + 6 = -1(x - 3)$, identify the slope and a point on the line." | "The slope is $m=-1$ and a point on the line is $(3, -6)$." |
| "When graphing an equation like $y = 2x - 4$, what is the first point you should plot?" | "The first point to plot is the y-intercept, which is at $(0, -4)$." |
| "After plotting the y-intercept for $y = 2x - 4$, how do you use the slope ($m=2$) to find the next point?" | "From the y-intercept, you go up 2 units (rise) and to the right 1 unit (run)." |
| What is the key growth characteristic of a linear function? | "A linear function grows by equal differences over equal intervals, which means it has a constant rate of change." |
| What is the key growth characteristic of an exponential function? | An exponential function grows by equal factors (a constant percent rate) over equal intervals. |
| "According to the F-LE.3 standard, what is the long-term relationship between an exponentially increasing quantity and a linearly or quadratically increasing quantity?" | An exponentially increasing quantity will eventually exceed a quantity increasing linearly or quadratically. |
| "The standard form of a linear equation, $Ax + By = C$, is particularly useful for finding the _____." | x and y intercepts |
| "What type of line is represented by the equation $y = c$, where 'c' is a constant?" | A horizontal line. |
| "What type of line is represented by the equation $x = c$, where 'c' is a constant?" | A vertical line. |
| "Given the points $(2, 5)$ and $(5, 14)$, what is the slope of the line connecting them?" | The slope is 3. |
| "If a line's slope is $-4/7$, what is the slope of a perpendicular line?" | The slope of the perpendicular line is $7/4$. |
| "If a line's slope is $-3$, what is the slope of a parallel line?" | The slope of the parallel line is also $-3$. |
| "The point $(-3, 0)$ is an example of what kind of intercept?" | It is an x-intercept because the y-value is zero. |
| "The point $(0, 6)$ is an example of what kind of intercept?" | It is a y-intercept because the x-value is zero. |
| What does it mean for two lines to be perpendicular? | Perpendicular lines intersect at a right angle (90 degrees). |
| What does it mean for two lines to be parallel? | Parallel lines travel in the same direction and never intersect. |
| "To find the x-intercept for $3x - 2y = 6$, you would solve the equation _____." | $3x = 6$ |
| "To find the y-intercept for $3x - 2y = 6$, you would solve the equation _____." | $-2y = 6$ |
| "In the point-slope equation $y + 4 = -\frac{3}{2}(x + 1)$, what are the coordinates of the identified point?" | "The coordinates of the point are $(-1, -4)$." |
| "Which function type, linear or exponential, is represented by the equation $y = x^2 - 3$?" | "Neither, this is a quadratic function." |
| "A function that is eventually exceeded by exponential growth, as required for comparison in the standards, is a _____ function." | quadratic |
| The equation $y=2^x$ represents what type of function? | An exponential function. |
| The equation $y = 4x + 10$ represents what type of function? | A linear function. |
| "If you are graphing from point-slope form and run out of space on the graph in one direction, what is an alternative way to plot a point?" | "You can go backwards by reversing both the rise and run directions (e.g., up and left instead of down and right)." |
Created by:
J-Sllim-00