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Questions and Answers
What is the slope of the line that passes through the points (−58, 31) and (5, 10)?
What is the slope of the line that passes through the points (−58, 31) and (5, 10)?
- $-1.86$
- $-3.41$ (correct)
- $1.86$
- $3.41$
If the slope of the line is $-3.41$, what is the y-intercept when the line is expressed in slope-intercept form?
If the slope of the line is $-3.41$, what is the y-intercept when the line is expressed in slope-intercept form?
- $-7.9$
- $2.15$
- $28.3$
- $11.45$ (correct)
What is the slope-intercept form of the equation of the line that goes through the points (−58, 31) and (5, 10)?
What is the slope-intercept form of the equation of the line that goes through the points (−58, 31) and (5, 10)?
- $y = -3.41x - 7.9$ (correct)
- $y = 3.41x + 11.45$
- $y = -3.41x + 31$
- $y = -3.41x + 2.15$
To find the equation of the line, which calculations are necessary before writing the final equation in slope-intercept form?
To find the equation of the line, which calculations are necessary before writing the final equation in slope-intercept form?
Which of the following represents the correct formula to determine the slope between two points?
Which of the following represents the correct formula to determine the slope between two points?
To find the slope of the line between two points, use the formula: (y2 - y1) / (x2 - x1) where the points are (x1, y1) and (x2, y2). The first point is (−58, 31) and the second point is (5, ______).
To find the slope of the line between two points, use the formula: (y2 - y1) / (x2 - x1) where the points are (x1, y1) and (x2, y2). The first point is (−58, 31) and the second point is (5, ______).
The slope calculated from the points (−58, 31) and (5, 10) is ______.
The slope calculated from the points (−58, 31) and (5, 10) is ______.
Once the slope is determined, the equation of the line can be written in ______ form.
Once the slope is determined, the equation of the line can be written in ______ form.
In the equation of a line expressed in slope-intercept form, 'y=' is followed by the ______ and the y-intercept.
In the equation of a line expressed in slope-intercept form, 'y=' is followed by the ______ and the y-intercept.
After calculating the slope of -3.41, you can find the y-intercept by substituting one of the points into the equation y = mx + ______.
After calculating the slope of -3.41, you can find the y-intercept by substituting one of the points into the equation y = mx + ______.
Flashcards
Slope
Slope
The change in y divided by the change in x. It represents how much the y-value changes for every 1 unit change in the x-value.
Slope-intercept form
Slope-intercept form
A linear equation written in the form y = mx + b, where m is the slope and b is the y-intercept.
Y-intercept
Y-intercept
The point where a line crosses the y-axis.
Equation of a line
Equation of a line
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Finding the equation of a line
Finding the equation of a line
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Slope Formula
Slope Formula
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Study Notes
Finding the Equation of a Line
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To find the equation of a line passing through two points, first calculate the slope.
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The formula for the slope (m) of a line passing through points (x₁, y₁) and (x₂, y₂) is: m = (y₂ - y₁)/(x₂ - x₁)
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Substitute the given points (-58, 31) and (5, 10) into the slope formula: m = (10 - 31) / (5 - (-58)) m = -21 / 63 m = -1/3
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Now that we have the slope, we can use the point-slope form of a linear equation, which is: y - y₁ = m(x - x₁)
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Choose either point. Let's use (5, 10): y - 10 = (-1/3)(x - 5)
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Simplify the equation to slope-intercept form (y = mx + b): y - 10 = (-1/3)x + 5/3 y = (-1/3)x + 5/3 + 10 y = (-1/3)x + 5/3 + 30/3 y = (-1/3)x + 35/3
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Thus, the equation of the line in slope-intercept form is: y = -1/3x + 35/3
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