The way to calculate the equation of a line that includes the points (x,y) and (x1, y1) is to plug them into the equation y - y1 = m(x - x1) and solve for m, the slope of the line. The way to convert this to y = mx + b form is to plug one point and the slope into the same equation and solve for y.
Linear equations describe straight lines as they appear on a graph. Linear equations are most commonly described in slope-intercept form, written as y = mx + b. The letters x and y refer to the horizontal and vertical coordinates of any point on the line as it is graphed. The m refers to the slope of the line, and b refers to the x-coordinate of the point on the line when it crosses the y-axis.
The second most common form of linear equations is written in point-slope form as y - y1 = m (x - x1). This form is commonly used when only one point (x1, y1) and the slope m are known or when only two points on the line are known.
For straight vertical lines, the equation is x = x1, with no slope or y values given. This is because the slope for vertical lines is undefined, and for every value of y, x will always be the same number.