How to find Slope of parallel lines

Slope is used to describe the steepness, incline, gradient, or grade of a straight line. A higher slope value indicates a steeper incline. The slope is defined as the ratio of the "rise" divided by the "run" between two points on a line, or in other words, the ratio of the altitude change to the horizontal distance between any two points on the line or pair of straight lines. It is also always the same thing as how many rises in one run.The slope of a line in the plane containing the x and y axes is generally represented by the letter m, and is defined as the change in the y coordinate divided by the corresponding change in the x coordinate, between two distinct points on the line.The larger the absolute value of a slope, the steeper the line. A horizontal line has slope 0, a 45° rising line has a slope of +1, and a 45° falling line has a slope of -1. A vertical line's point slope form
is undefined meaning it has "no slope."

Question:-

How to find the slope of the line parallel to x+2y=10

Answer:-

Point to remember:- Parallel lines will have same slope
So we just have to find the slope of the given line.

x+2y = 10

subtract 'x' on both sides

2y = -x+10

divide by 2 on both sides

y = -x/2 + 5

So the slope is -1/2 for both the lines.

same way,we can also find all points having an x-coordinate of 2 whose distance from the point 2 1 is 5

Problem on Solving a Function and Show Graphical Representation for the Function

Relations and functions are the dependent concepts of math where the value of a variable is dependent on the other variable in the given function. It is expressed in terms of graphical representation as shown in the below example

Topic : Solving a Function and expressing graphically

In the given function variable 'x' is the independent value and y is the dependent one.

Problem : a) If y = √x −1, Find the values for x = 0, 1, 2, 3, 4.Round to three decimal places where necessary.
b) Explain why no negative values are chosen as values to substitute
in for x.
c) Draw a graphical representation for the values.

(a)Solution :

When x = 0
y = √x – 1
= √0 – 1
= 0 – 1
= -1

When x = 1
y = √x – 1
= √1 – 1
= 1 – 1 and y = -1 - 1
= 0 and y = -2

When x = 2
y = √x – 1
= √2 – 1
= 1.414 – 1 and y = -1.414 - 1
= 0.414 and y = -2.414

When x = 3
y = √x – 1
= √3 – 1
= 1.732 – 1 and y = -1.732 - 1
= 0.732 and y = -2.732

When x = 4
y = √x – 1
= √4 – 1
= 2 – 1 and y = -2 - 1
= 1 and y = -3

(b) Solution :
No negative values are chosen for x because square root of a negative
number is imaginary and is not defined in real space.

(c) Solution :

For more help contact geometry help or algebra help.