What does b represent in the equation of a line in the form y = mx + b?

Solution:

Given, y = mx + b

The equation of the straight line in slope-intercept form is given by y = mx + b.

Where, y indicates how far up or down is the line

x indicates how far along is the line

b indicates the value of y when x = 0

m indicates how steep the line is

m is determined by (difference in y coordinates)/(difference in x coordinates)

m = (y₂ - y₁)/(x₂ - x₁)

In other words, ‘b’ is the point where the line intersects the y-axis.

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 form x = a.

For example:

Consider the equation 2x + 3y = 6

Rewrite the equation in standard form,

3y = -2x + 6

y = (-2/3)x + 6

Therefore, the value of b is 6.

What does b represent in the equation of a line in the form y = mx + b?

Summary:

In the equation of a line in the form y = mx + b, ‘b’ represents the point where the line intersects the y-axis.