Final answer:
To convert a line's equation from slope-intercept to point-slope form, identify the slope (m) and any point (x1, y1) on the line, such as the y-intercept. For a line with slope 3 and y-intercept 9, the slope-intercept form y = 3x + 9 becomes y - 9 = 3(x - 0) in point-slope form.
Step-by-step explanation:
To convert from slope-intercept form to point-slope form, you must identify the slope (m) and a specific point (x1, y1) through which the line passes. If we start with the slope-intercept form of a line, y = mx + b, where m is the slope and b is the y-intercept, we can easily translate this into the point-slope form.
For instance, given a line where the slope (m) is 3 and the y-intercept (b) is 9, its slope-intercept form is y = 3x + 9. To write this in point-slope form, you first choose a point on the line. A convenient point to choose is the y-intercept, which is (0, 9) in this case. Then, you plug the slope and the coordinates of the point into the point-slope formula, which is y - y1 = m(x - x1). This results in y - 9 = 3(x - 0), which is the point-slope form of the equation.
The point-slope form is particularly useful when you have a slope and a specific point, and you wish to write the equation of a line. It is a straightforward method for expressing the relationship between the coordinates of any point on the line, its slope, and a known point.