Final answer:
To determine the slope and y-intercept of a line from two points, calculate the slope by dividing the change in y by the change in x (rise over run), and solve for the y-intercept by substituting one of the points' coordinates into the equation y = mx + b.
Step-by-step explanation:
The equation of a line in slope-intercept form is given by y = mx + b, where m is the slope of the line and b is the y-intercept. To determine the values of m (slope) and b (y-intercept) using the coordinates of two points on the line, follow the steps:
- Calculate the slope (m) by taking the difference in the y-values of the two points (denoted as Y2 - Y1) and dividing it by the difference in the x-values of the two points (denoted as X2 - X1). This is known as the rise over run.
- Use one of the points and the slope to solve for the y-intercept (b). This is done by substituting the x and y coordinates of the point into the equation and solving for b.
For example, if a line goes through points (1,2) and (4,11), the slope m would be calculated as (11-2)/(4-1) = 3. Then, using the point (1,2), we substitute into the equation: 2 = 3(1) + b, which gives us b = -1. Hence, the equation of the line is y = 3x - 1.