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Questions and Answers
What is the first step to find the slope of the line that goes through the points (−58, 31) and (5, 10)?
What is the first step to find the slope of the line that goes through the points (−58, 31) and (5, 10)?
What is the calculated slope of the line going through the points (−58, 31) and (5, 10)?
What is the calculated slope of the line going through the points (−58, 31) and (5, 10)?
After finding the slope, what is the next step to write the equation in slope-intercept form?
After finding the slope, what is the next step to write the equation in slope-intercept form?
If the slope found is $\frac{-1}{3}$ and one of the points is (5, 10), what is the y-intercept of the line?
If the slope found is $\frac{-1}{3}$ and one of the points is (5, 10), what is the y-intercept of the line?
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What is the final slope-intercept form of the equation of the line that passes through the points (−58, 31) and (5, 10)?
What is the final slope-intercept form of the equation of the line that passes through the points (−58, 31) and (5, 10)?
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Study Notes
Finding the Equation of a Line
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To find the equation of a line in slope-intercept form (y = mx + b), we need the slope (m) and the y-intercept (b).
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The slope (m) is calculated using the formula: m = (y₂ - y₁) / (x₂ - x₁) where (x₁, y₁) and (x₂, y₂) are two points on the line.
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Using the points (-58, 31) and (5, 10):
- x₁ = -58, y₁ = 31
- x₂ = 5, y₂ = 10
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Calculate the slope:
- m = (10 - 31) / (5 - (-58)) = (-21) / (63) = -1/3
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Now that we have the slope (m = -1/3), we can use one of the points (e.g., (5, 10)) and the slope to find the y-intercept (b).
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Substitute the values into the slope-intercept form equation (y = mx + b):
- 10 = (-1/3) * 5 + b
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Solve for b:
- 10 = -5/3 + b
- b = 10 + 5/3
- b = 30/3 + 5/3 = 35/3
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The equation of the line in slope-intercept form is:
- y = (-1/3)x + 35/3
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Description
This quiz focuses on deriving the equation of a line in slope-intercept form using two given points. It covers calculating the slope and y-intercept, providing a clear understanding of the concepts involved. Complete the quiz to test your knowledge on this fundamental algebra topic.
