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Questions and Answers
What is the slope-intercept form of the equation of the line that passes through the point (1, -1) with a slope of -4?
What is the slope-intercept form of the equation of the line that passes through the point (1, -1) with a slope of -4?
y = -4x + 3
Using point-slope form, how would you write the equation for the line with slope -4 passing through (1, -1)?
Using point-slope form, how would you write the equation for the line with slope -4 passing through (1, -1)?
y + 1 = -4(x - 1)
If the slope of the line is -4, what does this indicate about the direction of the line?
If the slope of the line is -4, what does this indicate about the direction of the line?
The line decreases from left to right.
What is the y-intercept of the line that passes through (1, -1) with a slope of -4?
What is the y-intercept of the line that passes through (1, -1) with a slope of -4?
How does the slope of -4 affect the steepness of the line compared to a slope of -1?
How does the slope of -4 affect the steepness of the line compared to a slope of -1?
Flashcards
Slope
Slope
A line's steepness or direction. It represents the change in y-values divided by the change in x-values.
Point
Point
A specific point on a line, expressed as a pair of coordinates (x, y).
Equation of a line
Equation of a line
A mathematical equation that describes the relationship between x and y values on a line.
Slope-intercept form: y = mx + b
Slope-intercept form: y = mx + b
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Y-intercept
Y-intercept
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Study Notes
Finding the Equation of a Line
- A line passes through the point (1, -1).
- The slope of the line is -4.
- Use the point-slope form of a linear equation: y - y₁ = m(x - x₁), where m is the slope and (x₁, y₁) is a point on the line.
- Substitute the given values: y - (-1) = -4(x - 1)
- Simplify the equation: y + 1 = -4x + 4
- Solve for y: y = -4x + 3
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