Final answer:
To write the slope-intercept form of a line using a point and slope, apply the point and slope to the formula y = mx + b by using the point-slope equation y - y1 = m(x - x1) to first solve for b, the y-intercept.
Step-by-step explanation:
To write the equation of a line in slope-intercept form using a given point and a slope, you would use the equation y = mx + b, where m represents the slope of the line and b represents the y-intercept. The slope describes the steepness of the line, or the rise over run; that is, how much y increases for a certain increase in x. To find the y-intercept, you use the coordinates of the given point and the slope.
For example, with a slope of 3 and a y-intercept of 9, the equation would be y = 3x + 9. If you have a certain point, let's say (x1, y1), and a slope m, you would plug these into the slope formula to get the y-intercept:
- Start with the point-slope form: y - y1 = m(x - x1).
- Apply the values of your point and slope.
- Rearrange the equation to get y = mx + b, solving for b.
This equation shows the relationship between the algebra of straight lines and their graphical representation on a coordinate plane with x on the horizontal axis and y on the vertical axis. From the graph, the y-intercept is where the line crosses the y-axis, and the slope is consistent throughout the line.