What is point slope form? How is it different than slope intercept form? Which one is better?
line with slope m through (h,k):
(y-k) = m(x-h)
line with slope m and y-intercept at (0,b):
y = mx+b
Neither is always better. Which to use depends on the data given or required.
Point slope form is a linear equation format that represents the equation of a line as:
y - y₁ = m(x - x₁)
In this equation, (x₁, y₁) represents the coordinates of a point on the line, and m represents the slope of the line. This form is generally used when you know the slope of the line and a point on the line.
On the other hand, slope intercept form is another linear equation format that represents the equation of a line as:
y = mx + b
In this equation, m still represents the slope of the line, and b represents the y-intercept, which is the point where the line crosses the y-axis. Slope intercept form is commonly used when you know the slope and the y-intercept of the line.
The main difference between point slope form and slope intercept form is the information they require to write the equation. Point slope form requires a specific point on the line and the slope of the line. Slope intercept form, on the other hand, requires the slope of the line and the y-intercept of the line.
Which form is better depends on the given information and the context of the problem. If you have a specific point on the line along with the slope, point slope form is more suitable. If you know the slope and the y-intercept, slope intercept form is more appropriate. It's important to choose the form that best fits the given information to simplify calculations and convey the equation accurately.