Step-by-step explanation:
The equation y - b = m(x - a) is a mathematical formula that describes the relationship between the x and y coordinates of a point on a line. The equation is called "point-slope form" because it uses the coordinates of a point on the line (point a) and the slope of the line (m) to describe the line.
The equation has three parts: y, b, and m(x - a).
The y part of the equation represents the y-coordinate of a point on the line. This value can change depending on the x-coordinate of the point.
The b part of the equation is the y-coordinate of a known point on the line. This value is fixed and does not change.
The m(x - a) part of the equation represents the slope of the line and the x-coordinate of the known point on the line. The slope is represented by m, and the x-coordinate of the known point is represented by a.
To use the equation to find the y-coordinate of a point on the line, you first need to know the x-coordinate of the point and the values of b, m, and a. Then, you can substitute these values into the equation and solve for y.
For example, if the x-coordinate of a point on the line is 5, the y-coordinate of a known point on the line is 2, the slope of the line is 3, and the x-coordinate of the known point is 1, then the y-coordinate of the point can be calculated as follows:
y - 2 = 3(x - 1)
y = 3x - 3 + 2
y = 3(5) - 3 + 2
y = 15 - 3 + 2
y = 14
Therefore, the y-coordinate of the point with x-coordinate 5 is 14.
In summary, the equation y - b = m(x - a) is a mathematical formula that describes the relationship between the x and y coordinates of a point on a line. The equation uses the coordinates of a known point on the line and the slope of the line to describe the line, and you can use it to find the y-coordinate of a point on the line if you know the x-coordinate of the point and the values of b, m, and a.