Final answer:
To find the slope-intercept form of a linear equation from two points, calculate the slope (m) by dividing the difference in y-coordinates by the difference in x-coordinates and solve for the y-intercept (b) using one of the points along with the slope.
Step-by-step explanation:
In the context of linear equations, the slope-intercept form is an equation of the form y = mx + b, where m represents the slope and b represents the y-intercept. To find the slope-intercept form using two points, you need to first calculate the slope (m) using the change in y-coordinates divided by the change in x-coordinates from the two points.
Then, you use one of the points and the slope to solve for the y-intercept (b), by substituting the x and y values of the point into the slope-intercept form and solving for b.
The independent variable is typically denoted as x, and represents the input or cause, while the dependent variable, denoted as y, represents the output or effect. In the provided Figure A1, the line graph demonstrates a linear relationship where the slope is defined as the rise over run, indicating how much the y-value changes for a unit change in x. The y-intercept is the point where the line crosses the y-axis, and represents the value of y when x is zero.
Here is how the concept is applied:
- Identify two points on the line, for example (x1, y1) and (x2, y2).
- Compute the slope as m = (y2 - y1) / (x2 - x1).
- Use either point and plug in the values into the equation y - y1 = m(x - x1), then solve for y to get the y-intercept b.
- Write the final slope-intercept form equation as y = mx + b.
The equation of the line can be used to predict future values, understand trends, and analyze the relationship between variables.