Point Slope Form
y-y₁=m(x-x₁)
Point-slope form is a linear equation used to describe the relationship between two variables, typically represented as x and y. In this form, the equation involves one point (x1, y1) and the slope of the line, which is represented as m. The equation is given as:
y – y1 = m(x – x1)
The point-slope form describes a line in terms of its slope and one point on the line. The slope, m, indicates how steep the line is, and the point (x1, y1) specifies a point on the line.
To use point-slope form to write an equation, you need to know the slope of the line and a point it passes through. You can substitute the values into the equation and simplify to get the equation of the line in point-slope form.
For example, if you know that a line has a slope of 2 and passes through the point (3, 5), the equation in point-slope form would be:
y – 5 = 2(x – 3)
You can simplify this equation to slope-intercept form (y = mx + b) by solving for y:
y – 5 = 2x – 6
y = 2x – 1
Now the equation can be used to find the y-value for any given x, or the x-value for any given y, on the line represented by the equation.
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