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Questions and Answers
What is the slope of the line passing through the points $(2, 5)$ and $(4, 9)$?
What is the slope of the line passing through the points $(2, 5)$ and $(4, 9)$?
- $3$
- $1/2$
- $1$
- $2$ (correct)
A line has a slope of 2 and passes through the point (2, 5). What is the y-intercept (b) of this line?
A line has a slope of 2 and passes through the point (2, 5). What is the y-intercept (b) of this line?
- 1 (correct)
- 2
- 3
- 0
Which of the following equations represents the line passing through the points (2, 5) and (4, 9)?
Which of the following equations represents the line passing through the points (2, 5) and (4, 9)?
- $y = x + 3$
- $y = 2x + 1$ (correct)
- $y = 2x - 1$
- $y = 3x - 1$
Consider a line with the equation $y = 2x + b$. If this line passes through (4, 9), what is the value of y when x = 0?
Consider a line with the equation $y = 2x + b$. If this line passes through (4, 9), what is the value of y when x = 0?
How would the equation of the line change if the point (2, 5) was shifted to (2, 7), while the second point (4,9) remained the same?
How would the equation of the line change if the point (2, 5) was shifted to (2, 7), while the second point (4,9) remained the same?
Flashcards
What is slope (m)?
What is slope (m)?
The change in y divided by the change in x between two points on a line. m = (y2 - y1) / (x2 - x1)
What is slope-intercept form?
What is slope-intercept form?
A way to write a linear equation: y = mx + b, where m is the slope and b is the y-intercept.
What is the y-intercept (b)?
What is the y-intercept (b)?
The point where the line crosses the y-axis (where x = 0).
How do you find the equation of a line?
How do you find the equation of a line?
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Equation of the line through (2, 5) and (4, 9)
Equation of the line through (2, 5) and (4, 9)
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Study Notes
- The problem requires finding the equation of a line in slope-intercept form given two points.
- The slope-intercept form of a line is y = mx + b, where m is the slope and b is the y-intercept.
Calculating the Slope (m)
- The slope (m) can be calculated using the formula: m = (y2 - y1) / (x2 - x1).
- Given points (2, 5) and (4, 9), let (x1, y1) = (2, 5) and (x2, y2) = (4, 9).
- Substituting the values, m = (9 - 5) / (4 - 2) = 4 / 2 = 2.
- Therefore, the slope m = 2.
Finding the Y-Intercept (b)
- Substitute the slope (m = 2) and one of the points, say (2, 5), into the equation y = mx + b.
- Substituting, 5 = 2 * 2 + b.
- Simplifying, 5 = 4 + b.
- Solving for b, b = 5 - 4 = 1.
- Therefore, the y-intercept b = 1.
Writing the Equation
- Now that we have m = 2 and b = 1, we can write the equation in slope-intercept form.
- The equation is y = 2x + 1.
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Description
Explanation of how to find the equation of a line in slope-intercept form when given two points on the line. The slope is calculated, then the y-intercept. Finally, the equation is written in slope-intercept form.
