Learn about Problems on Straight Lines

Define a straight line?

The gathering of certain points within two given sets of locations or even extending in number across two locations seems to be known as a straight line. A line seems to be a primitive object within the subject of geometry. These straight lines do not seem to have any characteristics other than its being one dimensional in its length.

Straight lines throughout Euclidean geometry seem to contain just one dimension in them, which seems to be the length; this has a property of infinite stretching in both directions of the given points indefinitely.

Brief on problems on straight lines?

Within a cartesian plane that seems to have a coordinate system, the equation of a straight line seems to be represented in an algebraic form that seems to represent two given points that together constitute a straight line. The several points that are present on the surface seem to form a line when combined together; these seem to get represented with variables in the form of x as well as y. These variables help in building an algebraic equation that represents the equation of a straight line. If there is a need to find a specific point on a line, one needs to find the equation of that line to find the result. The straight line seems to be a figure constructed by connecting two locations, for example, A (x1, y1) on the cartesian plane or B (x2, y2). The points of x and y are connected in a way that follows the shortest distance in between them. The linear equation that has the variables x and y have the following mathematical form:  ax + by = c.

The formula can be used to find the equation of a straight line, but it also seems to depend on the data currently provided. The following are the procedures one can follow to find the equation if some form of data is given:

• The coordinate points need to be represented with the letters x1, y1 and so on. The slope of the line needs to be represented with ‘m’.
• After noting down the given information, it needs to be substituted in the formula with respective values in their own places. There are different forms of the equation where these data can be substituted like,

1. The slope-intercept formula seems to be used to derive the equation of a straight line if its slope and intercept are on the y-axis.
2. Another type called the point-slope form is used to calculate the straight-line equation if the slope is given and one of its coordinate points that seem to lie on the line is given too.
3. The two-point format seems to be used to calculate an equation of a given straight line if the two points of coordinates present on it are given.
4. Reorganizing the variables in order to represent the line equation in a standard form or the other forms of line equations for which slope is required to be calculated.

The slope of the straight line

The slope seems to be one of the important variables while computing for an equation. The slope of a straight line seems to be a quantity that seems to represent two points or both the line’s X as well as Y coordinates, including its steepness as well throughout the subject of mathematics. The letter ‘m’ represents the slope value. The ratio of change vertically as well as horizontally of two points is represented by the slope as it represents two unique points on a cartesian plane that is used to compute the slope. 

• If the line seems to be continually growing from the left towards the right, it is considered a trend line. m > 0 indicates that the slope remains positive.
• If the opposite happens and the line seems to be decreasing and runs from the left towards the right, it seems to be called a diminishing line. m < 0 represents a negative slope.
• When the line seems to be a simple horizontal structure, the slope represents a 0, and the function remains constant.
• The vertical slope is undefined.

Example

Solve for the equation of a straight line that seems to pass through the coordinates (5, 4) and (-1, 2).

Solution: A point-slope formula needs to be used to find the solution, and to do that, one needs to find the slope.

Slope = (2-4)/(-1-5) = -2/4

After putting the values in there respective places is y – 4 = (-2/4) (x + 5)

⇒ y – 4 = -x/4 – 5/4

⇒ y + x/4 = 4 – 5/4

⇒ x + 4y = 11 (answer)

Conclusion

The article explains briefly about problems of straight-line equations, and it further talks about what straight-line equations represent and are calculated using different forms. The article also mentions a few terms related to straight lines, like slope of a straight line which is crucial for finding out equations.