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Questions and Answers
What is the y intercept of the line?
What is the x intercept of the line?
What is the slope of the line?
For what value of x does f(x) = 0?
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What is the slope of the line that passes through the points (6, 3) and (-2, 1)?
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What is the y intercept of the line that passes through the points (-7, 2) and (5, -1)?
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The line y = 7 is:
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Create a table of values for the equation $y = \frac{3}{5}x - 3$, plot the points, and graph the equation.
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Write the equation of the line that passes through the points (4, 1) and (-3, -1).
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Find the x and y intercepts of the equation -2x + 5y - 12 = 8.
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A line has an x intercept of -5 and a y intercept of 3. Write an equation for the line.
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Write the equation of the line that is parallel to 8x - 2y = 12 and passes through (-2, 6).
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Write the equation of the line that is perpendicular to 8x - 2y = 12 and passes through (4, -2).
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Write an equation of a line that would be perpendicular to 3x + 4y = 15.
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For what value of x does f(x)=0 in the function f(x) = 4x + 3?
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A line passes through the points (6, 4), (1, -2), and (-4, -8). What is the equation of the line?
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Study Notes
Identifying Intercepts and Slope
- The y-intercept of a line is the point where the line crosses the y-axis.
- The x-intercept of a line is the point where the line crosses the x-axis.
- The slope of a line is a measure of its steepness. It is calculated as the change in y divided by the change in x.
- To find the x-intercept of a line, set y = 0 and solve for x.
- To find the y-intercept of a line, set x = 0 and solve for y.
Writing Equations
- The point-slope form of a linear equation is y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line.
- The slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept.
- To find the equation of a line that passes through two points, first find the slope using the slope formula: m = (y2 - y1) / (x2 - x1). Then use the point-slope form to write the equation.
- Parallel lines have the same slope.
- Perpendicular lines have slopes that are negative reciprocals of each other.
Graphing Linear Equations
- To graph a linear equation, you can use the slope-intercept form (y = mx + b). The y-intercept (b) gives you the starting point on the y-axis. Then, use the slope (m) to find another point on the line.
- You can also graph a linear equation by plotting two points on the line and connecting them with a straight line.
Applying Linear Equations to Real-World Situations
- Linear equations can be used to model real-world situations, such as the relationship between the number of hours worked and the amount of money earned.
- In a linear equation, the slope represents the rate of change and the y-intercept represents the starting value.
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Description
This quiz covers the key concepts of intercepts, slope, and writing equations of linear lines. You'll learn how to identify x and y-intercepts, calculate slope, and formulate equations in point-slope and slope-intercept forms. Test your understanding of these fundamental principles in linear equations!
