The equation 2x - y = C defines a family of lines, one line for each value of C. On one set of coordinate axes, graph the members of the family when C = - 4, C = 0, and C = 2. Can you draw a conclusion from the graph about each member of the family?

Q: Graph the line y=5x+4 with only two points

A: The given equation is  y=5x+4

Q: On the same axes, graph the lines x = 0, x = 2, and x = — 2.

A: Given: x=0, x=2, x=-2 Graph of given equations of lines on same rectangular coordinate system can be…

Q: Graph y = x2 + 4 by plotting points.

A: Given: y=x2+4

Q: Write an equation for the line graphed below -6 -5 -4 -3 -2 -1 In 5 4 3 2- 14 -1- -2 -B- -4 -5 -6 y…

A: The given graph is straight line. The equation of a straight line with slope m and y-intercept c…

Q: Find an oquation of the line containing the point (-2, 6) and a. parallel to 2x +y-5 perpendicular…

A:

Q: Graph the line x= 3.

A: Given,           The line is x=3.

Q: Graph the line x=2

A:

Q: E. Write an equation with a graph that looks like y = |x|, with the point of the V-shaped graph at…

A:

Q: Graph the line through (-2,-7), m=6

A: First plot (-2, -7). Then for m=6. Go 6 unit up and 1 unit right. (-2+1, -7+6)=(-1,-1)

Q: a farmer finds there is a linear relationship between the number of beans stalks, n, she plants, and…

A: The number of beans stalks is n and the yield is y. The linear relationship is in the form of…

Q: On the same axes, graph the lines y = 0, y = 3, and y = —3.

A: The graph of line y = k is always parallel to x-axis and will be at a distance of 'k' units from x…

Q: The y-coordinate is the second number of an ordered pair and represents the point's horizontal…

A:

Q: Find the equation of the line that goes through (2,6) and (3,4). Graph the line

A: The equation of line passing through two points (x1,y1) and (x2,y2) is given by, (y - y1) = m (x -…

Family of Curves

A family of curves is a group of curves that are each described by a parametrization in which one or more variables are parameters. In general, the parameters have more complexity on the assembly of the curve than an ordinary linear transformation. These families appear commonly in the solution of differential equations. When a constant of integration is added, it is normally modified algebraically until it no longer replicates a plain linear transformation. The order of a differential equation depends on how many uncertain variables appear in the corresponding curve. The order of the differential equation acquired is two if two unknown variables exist in an equation belonging to this family.

XZ Plane

In order to understand XZ plane, it's helpful to understand two-dimensional and three-dimensional spaces. To plot a point on a plane, two numbers are needed, and these two numbers in the plane can be represented as an ordered pair (a,b) where a and b are real numbers and a is the horizontal coordinate and b is the vertical coordinate. This type of plane is called two-dimensional and it contains two perpendicular axes, the horizontal axis, and the vertical axis.  

Euclidean Geometry

Geometry is the branch of mathematics that deals with flat surfaces like lines, angles, points, two-dimensional figures, etc. In Euclidean geometry, one studies the geometrical shapes that rely on different theorems and axioms. This (pure mathematics) geometry was introduced by the Greek mathematician Euclid, and that is why it is called Euclidean geometry. Euclid explained this in his book named 'elements'. Euclid's method in Euclidean geometry involves handling a small group of innately captivate axioms and incorporating many of these other propositions. The elements written by Euclid are the fundamentals for the study of geometry from a modern mathematical perspective. Elements comprise Euclidean theories, postulates, axioms, construction, and mathematical proofs of propositions.

Lines and Angles

In a two-dimensional plane, a line is simply a figure that joins two points. Usually, lines are used for presenting objects that are straight in shape and have minimal depth or width.