Point Slope Form
Point-slope form is a way to express the equation of a straight line
Point-slope form is a way to express the equation of a straight line. It provides a concise and convenient representation by using a specific point on the line and the slope of the line. The general form of the point-slope equation is:
y – y1 = m(x – x1)
where (x1, y1) is a known point on the line, and m is the slope of the line.
To understand and use the point-slope form, follow these steps:
Step 1: Identify the given information.
You need two pieces of information: a known point on the line (x1, y1), and the slope (m) of the line. The known point can be in any format, such as (2, 3) or (-1, 5), and the slope can be in any form, such as a fraction or decimal.
Step 2: Write the equation.
Once you have the known point and slope, substitute their values into the point-slope form equation:
y – y1 = m(x – x1)
Replace y1 with the y-coordinate of the known point, and x1 with the x-coordinate. Also, replace m with the given slope.
For example, consider the following problem: Find the equation of a line that passes through the point (4, 6) and has a slope of -2.
Substituting the values into the point-slope form equation, we get:
y – 6 = -2(x – 4)
Step 3: Simplify the equation if necessary.
Distribute the value of -2 to the terms inside the parentheses:
y – 6 = -2x + 8
Step 4: Get the equation in the desired form.
If required, you can rewrite the equation in standard form (Ax + By = C) or slope-intercept form (y = mx + b). To convert the point-slope form to slope-intercept form, isolate y by moving the other terms to the other side of the equation:
y = -2x + 14
Now the equation is in slope-intercept form.
In conclusion, the point-slope form is a useful way to express the equation of a line when you know a specific point on the line and the slope of the line. By following the steps outlined above, you can convert the given information into an equation that describes the line accurately.
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