Podcast
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)?
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?
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)?
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?
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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?
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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, ______).
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The slope calculated from the points (−58, 31) and (5, 10) is ______.
The slope calculated from the points (−58, 31) and (5, 10) is ______.
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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.
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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.
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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 + ______.
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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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Description
This quiz explores how to find the equation of a line using two points. It covers the calculation of slope and how to apply the point-slope form to derive the slope-intercept form. Test your understanding of these fundamental concepts in algebra.
