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Since there are no given triplets, none of them!
Using the equation below, select the ordered triple that correctly indicates where the plane cuts the x-axis.3x+4y+8z=12
It is a linear equation in two variables, x and y. Any point on the line defined by the equation will satisfy the equation and conversely, any ordered pair that satisfies the equation will represent a point, in the Cartesian plane, will be on the line.
It is not. It is called a LINEAR equation. This is because the word linear refers to a line and, if the solutions of the equation, in the form of ordered pairs (x,y), were plotted on a Cartesian plane, they would all lie on a straight line.
An equation of a parabola in the x-y plane, is one possibility.
Since there are no given triplets, none of them!
Using the equation below, select the ordered triple that correctly indicates where the plane cuts the x-axis.3x+4y+8z=12
It is a linear equation in two variables, x and y. Any point on the line defined by the equation will satisfy the equation and conversely, any ordered pair that satisfies the equation will represent a point, in the Cartesian plane, will be on the line.
7x + 2y + 3z = 42At the z-axis, 'x' and 'y' are both zero.0 + 0 + 3z = 42z = 14The coordinates of the z-intercept (the 'ordered triple') are (0, 0, 14)
The list of choices that accompanies the question is really short.2x + 3y + 6z = 54At the y-intercept, 'x' and 'z' are zero.3y = 54y = 18
It is not. It is called a LINEAR equation. This is because the word linear refers to a line and, if the solutions of the equation, in the form of ordered pairs (x,y), were plotted on a Cartesian plane, they would all lie on a straight line.
7x + 2y + 3z = 42 The plane intersects each coordinate plane, but since you are interested to know where the plane cuts y-axis, this will happen when the plane cuts xy-plane or yz-plane. So you can set z = 0, or x = 0. So, set z = 0, then the plane will cuts the xy-plane along the line 7x + 2y = 42. If x = 0, then the y-intercept is 42/2 = 21.
A suitable equation for that would be y is equal to negative 2 times x plus five
An equation of a parabola in the x-y plane, is one possibility.
12
y equals x plus 5 is the equation of a straight line in the x-y plane.
It is a horizontal line in the Cartesian plane, or a vertical line in the complex plane. The reason is that these points satisfy the equation while no others do.