Question

How do you find b in $y = mx + b$?

Answer 1

The standard form $y = mx + b$ is where m is the slope and b is the y-intercept. For calculating y-intercept we will take $x = 0$ because it is equivalent to the y-coordinate of the point.

Complete step by step answer:
Let the slope = $m$
Let the point = $({x_1},{y_1})$
the standard form of $y = mx + b$ becomes ${y_1} = {x_1}m + b$
For calculating y-intercept we will take $x = 0$ because it is equivalent to the y-coordinate of the point.
now you take the point $(x,y) = (0,{y_1})$that is on the line (has to be on the line) and replace x and y in the equation with it.
The equation becomes
${y_1} = 0 \times m + b \\\ {y_1} = b \\\$
So this way you can find y-intercept.

Note: if two points were given in questions so you can directly use the below equation.
$b = \dfrac{{{x_2}{y_1} - {x_1}{y_2}}}{{{x_2} - {x_1}}}$
Here, $({x_1},{y_1})$ and $({x_2},{y_2})$ are points on line
You do not have to memorize this formula, we can let one of two points be on the y-axis.
In this case, let that be the first point,
So ${x_1} = 0$
So here again we get ${y_1} = b$.