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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)?
- Subtract the y-coordinates of the points.
- Subtract the x-coordinates of the points.
- Calculate the vertical distance between the points.
- Use the formula $m = \frac{y_2 - y_1}{x_2 - x_1}$. (correct)
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)?
- $\frac{21}{63}$
- $\frac{-21}{-63}$
- $\frac{-21}{63}$ (correct)
- $\frac{21}{-63}$
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?
- Find the midpoint of the two points.
- Calculate the distance between the two points.
- Use the slope and one of the points to find the y-intercept. (correct)
- Convert to standard 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?
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)?
Flashcards
Slope-intercept Form
Slope-intercept Form
An equation of a line written in the form y = mx + b, where 'm' represents the slope and 'b' represents the y-intercept.
Slope of a Line
Slope of a Line
The measure of a line's steepness, calculated by dividing the change in y-coordinates by the corresponding change in x-coordinates.
Y-intercept
Y-intercept
The point where a line crosses the y-axis. It has an x-coordinate of 0.
Find the Slope
Find the Slope
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Find the Y-intercept
Find the Y-intercept
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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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