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The equation of a straight line can be written in many other ways. Another popular form is the Point-Slope Equation of a Straight Line. 358,359,517,518, 1156, 1157 ...
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May 19, 2023 · Definition: POINT-SLOPE FORM OF A LINE. If line L passes through the point (x1, y1) and has slope m, then the equation of the line is y − y1 = m(x − x1) This form of the equation of a line is called the point-slope form. To use the point-slope form of a line, follow these steps.
- Overview
- Calculating the Equation with One Point and the Slope
- Finding the Equation Using Two Points
Finding the equation for a line is a common problem in geometry and trigonometry. There are two common situations where you are asked to find the equation for a line: either you'll be provided with one point on the line and the slope of the line, or you'll be provided two points on the line. In either case, finding the equation for that line isn't ...
Plug the slope in for
This is known as the point-slope formula.
The point-slope formula uses the slope and the coordinates of a point along the line to find the y-intercept. Use the slope in place of
For example, if you know the slope of the line is 2, then your formula will look like this:
with the coordinates of the point.
Use the coordinates you’re given as (x
The ordered pairs of the coordinates you have are listed as (x, y). Use the first set of coordinates as (x
) and the second set as (x
Plug the numbers into the formula
For example, if your coordinates are (3, 8) and (7, 12), the formula would read:
= (12-8)/ (7-3) = 4/4 =
In this case, your slope, or
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The equation of a horizontal line (a line parallel to the x-axis) is found using the general equation: y = b, where b is the y-coordinate of any point lying on the line. Similarly, the equation of a vertical line (a line parallel to the y-axis ) can be given as: x = a , where, a is the x-coordinate of any point lying on the given line.
Depending on the information provided, you can choose the form to determine the equation of a line. Step 1: Notice the data provided in the given problem. Step 2: Choose the appropriate form of the equation. If the coordinates of one point on the line (x 1, y 1) and the slope m are given, use the point-slope form.
- The equation of the x-axis is y = 0. The equation of the y-axis is x = 0.
- The slope of a line that passes through the points (x1, y1) and (x2, y2) is $\frac{(y_{2} - y_{1})}{(x_{2} - x_{1})}$.
- The slope-intercept form is given by y = mx + b, where m is the slope and b is the y-intercept. It is special because you can easily identify the s...
- The equation of a straight line is a linear algebraic equation that defines the relationship between coordinates of every point on the line and pro...
- If you know the coordinates of two points on the line, use the Two-Points form of the equation of a line.
General Equation of a Line. The general equation of a line in two variables of the first degree is represented as. Ax + By +C = 0, A, B ≠ 0 where A, B and C are constants which belong to real numbers. When we represent the equation geometrically, we always get a straight line. Below is a representation of straight-line formulas in different ...
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The equation of a straight line is commonly written as. y = mx + b. where m is the slope and b is the y-intercept. The slope determines how steep the line is. The y-intercept tells us the point at which the line intersects the y-axis. The x and y tell us the position relative to the x- and y-axes respectively.
