The Equation Of A Straight Line
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A straight line is the simplest graph there is, and yet it underlies an enormous amount of mathematics. Its entire behaviour is captured by two numbers: a gradient that fixes its steepness and an intercept that fixes its position. Master the equation of a line and coordinate geometry opens up.
In this lesson you will use the two standard forms, \(y=mx+c\) and \(y-y_1=m(x-x_1)\), to find the equation of a line from a gradient and a point, or from two points. These are the everyday tools of the coordinate geometry section.
Awọn Afojusun
- Use the equation of a straight line in the forms y = mx + c and y - y1 = m(x - x1).
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- In y = mx + c, the letter c represents the: A. gradient B. y-intercept C. x-intercept D. midpoint Answer: B
- The equation of the line with gradient 2 through (3, 4) is: A. y = 2x - 2 B. y = 2x + 2 C. y = 2x - 10 D. y = 2x + 4 Answer: A
- The gradient of the line through (1, 2) and (4, 11) is: A. 2 B. 3 C. 9 D. 1/3 Answer: B
- The equation of the line through (1, 2) and (4, 11) is: A. y = 3x - 1 B. y = 3x + 1 C. y = x + 1 D. y = 3x - 7 Answer: A
- Which is the point-gradient form of a line? A. y = mx + c B. y - y1 = m(x - x1) C. y = m + cx D. x = my + c Answer: B
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Linear Functions
Represent a linear function.
"College Algebra: Linear Functions" by OpenStax, OpenStax, Rice University, licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). Source: https://openstax.org/books/college-algebra/pages/4-1-linear-functions. Access for free at https://openstax.org/books/college-algebra/pages/1-introduction
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