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To avoid this vicious circle certain concepts must be taken as primitive concepts; terms which are given no definition. When the line concept is a primitive, the behaviour and properties of lines are dictated by the axioms which they must satisfy.

In a non-axiomatic or simplified axiomatic treatment of geometry, the concept of a primitive notion may be too abstract to be dealt with.

In this circumstance it is possible that a description or mental image of a primitive notion is provided to give a foundation to build the notion on which would formally be based on the unstated axioms.

Descriptions of this type may be referred to, by some authors, as definitions in this informal style of presentation. These are not true definitions and could not be used in formal proofs of statements. The "definition" of line in Euclid's Elements falls into this category.

In Euclidean geometry[ edit ] See also: Euclidean geometry When geometry was first formalised by Euclid in the Elementshe defined a general line straight or curved to be "breadthless length" with a straight line being a line "which lies evenly with the points on itself". In fact, Euclid did not use these definitions in this work and probably included them just to make it clear to the reader what was being discussed.

In modern geometry, a line is simply taken as an undefined object with properties given by axioms[6] but is sometimes defined as a set of points obeying a linear relationship when some other fundamental concept is left undefined. In an axiomatic formulation of Euclidean geometry, such as that of Hilbert Euclid's original axioms contained various flaws which have been corrected by modern mathematicians[7] a line is stated to have certain properties which relate it to other lines and points.

For example, for any two distinct points, there is a unique line containing them, and any two distinct lines intersect in at most one point. In higher dimensions, two lines that do not intersect are parallel if they are contained in a planeor skew if they are not.

Any collection of finitely many lines partitions the plane into convex polygons possibly unbounded ; this partition is known as an arrangement of lines.

On the Cartesian plane[ edit ] Lines in a Cartesian plane or, more generally, in affine coordinatescan be described algebraically by linear equations. In two dimensionsthe equation for non-vertical lines is often given in the slope-intercept form:Converting Equations to the Slope-Intercept Formula.

Let’s say we are given an equation in a form other than \(\boldsymbol{y=mx+b}\) and we were asked to graph metin2sell.com’s graph the line: \(x=7y+3\) We know that this equation is not in the slope-intercept form, and we must use what we’ve learned about algebra to somehow get it in the form we know.

Example: Write the equation of a line with a slope of 5 and a y-intercept of (0, -7). Since m = 5 and (0, -7) is the y-intercept, b = -7, then substituting into the form will give us.

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Equations that are written in slope intercept form are the easiest to graph and easiest to write given the proper information. Continue reading for a couple of examples! Example 1: Writing an Equation Given the Slope and Y-Intercept. Write the equation for a line that has a slope of -2 and y-intercept of 5. Write an equation in slope. Ask Math Questions you want answered Share your favorite Solution to a math problem Share a Story about your experiences with Math which could inspire or help others. You may already be familiar with the "y=mx+b" form (called the slope-intercept form of the equation of a line). It is the same equation, in a different form! The "b" value (called the y-intercept) is where the line crosses the y-axis.

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Some examples of linear equations in slope-intercept form: You could have y = 2x + 1; you could have y = -3x; and you could have y = (2/3)x - 6. Write the point-slope equation of the line that passes through (7, 3) (7,3) (7, 3) left parenthesis, 7, comma, 3, right parenthesis whose slope is 2 2 2 2.

Explain Want to try more problems like this? A positive attitude is an important aspect of the affective domain and has a profound effect on learning. Environments that create a sense of belonging, support risk taking and provide opportunities for success help students to develop and maintain positive attitudes and self-confidence.

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Gradient Slope Intercept Form | Passy's World of Mathematics