X% Of Y Is Increased By X%. What Is The Result In Terms Of X And Y?

y=mx+b

y = mx + b is the slope intercept class of writing the equation of a straight line. In the equation 'y = mx + b', 'b' is the betoken, where the line intersects the 'y centrality' and 'm' denotes the slope of the line. The slope or slope of a line describes how steep a line is. It can have either a positive or a negative value. When a standard form of a linear equation is of the course Ax + By = C, where 'x' and 'y' and 'C' are variables and 'A', 'B' are constants, the slope-intercept form is the nigh preferred way of expressing a straight line due to its simplicity, as it is very easy to find the slope and the 'y intercept' from the given equation.

i.	Pregnant of y = mx + b
2.	How to Find y = mx + b?
3.	Writing an Equation in the Slope Intercept Form
4.	Solved Examples on y mx b
5.	Exercise Questions on y mx b
6.	FAQs on y mx b

Meaning of y = mx + b

y = mx + b is the slope-intercept form of a staight line. In the equation y = mx + b for a straight line, m is called the slope of the line and b is the y-intercept of a line. y = mx+b, where

y ⇒ how far up or downwardly is the line,

x ⇒ how far along is the line,

b ⇒ the value of y when x = 0 and

g ⇒ how steep the line is.

This is determined by thousand = (difference in y coordinates)/ (difference in ten coordinates). Notation that deviation in y coordinates is indicated every bit rise or fall and divergence in ten coordinates is indicated every bit run.

y mx b, the equation of a straight line in the slope-intercept form.

How To Find y = mx + b?

y = mx + b is the formula used to discover the equation of a straight line, when we know the gradient(m) and the y-intercept (b) of the line. To determine m, we utilise a formula based on the calculations. Permit's derive this formula using the equation for the gradient of a line. Let us consider a line whose slope is 'm' and whose y-intercept is 'b'. Let (x,y) be any other random point on the line whose coordinates are non known. Nosotros obtain the graph as follows.

y-intercept of a line

We know that the equation for the slope of a line in the slope-intercept form is y = mx+b

Rewriting this, we get m = (y-b) / ten

Thus the formula to find k = change in y/ change in 10

finding slope of a line

Permit united states derive the formula to find the value of the gradient if 2 points \((x_{1},y_{ane})\) and \((x_{2},y_{two})\) on the direct line are known. So nosotros have \(y_{i} = mx_{1} + b\) and \(y_{2} = mx_{2} + b\)

We know that, slope = alter in y/ change in ten

Substituting the values of y_i and y_ii, we become \[\begin{marshal}\dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}&= \dfrac{(mx_{ii}+b) - (mx_{1}+b)}{x_{2}-x_{1}}\\\\&=\dfrac{mx_{two}-mx_{ane}}{x_{ii}-x_{1}}\\\\&= \dfrac{one thousand(x_{2}-x_{1})}{x_{two}-x_{ane}}\\\\ &=m\end{align}\]

Thus nosotros detect that the slope (g) is calculated as (change in y)/ (modify in x)

yard = (difference in y coordinates)/ (deviation in x coordinates)

To observe the y-intercept or 'b', substitute the value of 'x' as 0 in the equation of a straight line, which is of the form Ax + By + C = 0. Consider an equation of a straight line : 3x + 5y = 10. To notice the y-intercept, substitute the value of 'x' as 0 in the equation and solve for 'y'. On substituting 'x = 0' in the equation 3x + 5y =10, we go, 3(0) + 5y = ten
⇒5y = x and thus y = 10/5 ⇒ y = 2 or 'b' = 2.

Writing an Equation in The Slope Intercept Form

If the slope 'grand' and y-intercept 'b' are given, and so the equation of the straight line can be written in the form of 'y = mx +b'. For example, if the slope(k) for a line is ii and the y-intercept 'b' is -1, and then the equation of the directly line is written as y = 2x - 1. The slope value can be positive or negative. As we discussed in the earlier sections, in y = mx + b, 'm' represents the slope of the equation. To find the slope of a line, given its equation, we take to rearrange its terms to the slope-intercept form y = mx + b. Here, 'k' gives the gradient and 'b' gives the y-intercept of the equation.

Let united states of america consider the equation 2x + 3y = half dozen. We are required to find the slope and the y-intercept from the equation which is of the form Ax + By = C

We rewrite the standard form of the equation of the line to the gradient-intercept grade y = mx + b.

2x + 3y = 6
3y = 2x + 6
y = (-ii/iii) ten + two

Comparing the final equation with y = mx + b, we obtain the slope of the equation is m = -2/three and the y-intercept of the equation is, b = 2 or (0,two).

Important Notes:

The equation of the slope-intercept grade of a line whose slope is 'one thousand' and whose y-intercept is 'b' or (0,b) is y = mx + b.
The equation of a horizontal line passing through (a,b) is of the form y = b.
The equation of a vertical line passing through (a,b) is of the grade x = a.
m is calculated using the formula rise over run or (modify in y)/ (change in x)

Topics Related to y = mx + b

Bank check out some interesting articles related to y = mx + b.

Linear Equation Formula
Equation of a Straight Line
Linear Equations
Linear Equations and Half Planes
Point-gradient formula
Two Point Form

Example 1: Find the equation of the line whose graph contains the points (one,three) and (3,vii)

Solution:
The required equation of the line is y = mx + b
Using the formula for gradient, thousand = change in y / change in ten = \(\dfrac{y_{two}-y_{1}}{x_{ii}-x_{1}}\)
= (7-3)/ (3-1) = 4/2 ⇒ m = 2
To find the y-intercept b, nosotros consider any ane of the coordinates.
Let united states use(ane,3) and thousand = 2 and substitute the values in the equation \(y_{1} = mx_{1} + b\)
3 = ii(one) + b ⇒ b = iii - 2 = 1
Applying, m =2 and b = 1 in the equation of the line(y = mx + b), nosotros become y = 2x + ane Thus the equation of the direct line is y = 2x + 1
Example 2: Find the gradient-intercept form of a line with slope -2 and which passes through the point (-ane.4).

Solution:
We know that the gradient-intercept form of a line is y = mx + b.
Information technology is given that slope (m) = -2 and the coordinates through which the line is passing through is (-one,4). Substituting the given values in the slope-intercept course equation we get, four = (-2) (-i) + b.
4 = 2 + b b = 4 - 2 = ii.
The slope intercept form of the line is y = - 2 10 + 2.

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FAQs on y mx b

What is y = mx + b?

y = mx + b is a representation of equation of a straight line. Information technology is called as the gradient intercept form. 'chiliad' is referred to as the slope of the line, and 'b' refers to the 'y -intercept' of the line.

How to Find the Gradient of a Line?

For 2 coordinates, (x_i,y₁) and (x₂, y_two), the gradient of a line is the ratio of difference between the divergence between the y coordinates and the difference between x coordinates, also known as the rise over the run. The formula to discover the slope of a line is thousand = (y₂-y₁)/(x₂-x_ane)

What is Slope-Intercept Form?

The equation of a straight line which is of the form y = mx + b, is called the gradient intercept form. Hither 'grand' is the gradient of the line and 'b' is the point at which the line intercepts the y - axis. An instance for slope intercept grade equation is y = 3x + 5

What is a Line With a Negative Slope?

A line for which the slope in negative is said to motility from left to right in a graph. The slope of a line is found by the ration of difference in y-coordinates to the difference in x-coordinates. If this value is negative for a line, then the line has a negative gradient.

What Does the Slope of a Line Mean?

The direction of a line is described by its slope. The gradient can exist positive or negative, based on its direction. A negative slope moves downward from left to correct and a line with positive gradient moves in the upward direction from right to left.