Equation of a line: Graphs, Examples With Worksheet

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Equation of a line

  • Linear equations are a prominent part of algebra. It represents a relationship between two variables represented in a straight-line form.
  • A line equation is a basic notion that is common in different fields which include physics, engineering, economics, and data science among others.

In this article, we will discuss:

  1. What is the Equation of a Line?
  2. How to Find the Equation of a Line

Here is one more link to practice a few extra questions: Maths Genie Equation of a Line Questions

What is the Equation of a Line?

  • In mathematical terms, the equation for a line shows where the line is located in the Cartesian coordinate plane.
  • It is expressed as

y = mx + c,

where m is the gradient and c is the y-intercept.

Equation of a line Formula

  • In this example, m indicates line slope, and c shows y-intercept, which means where the line crosses the y-axis.
  • In case any (x, y) coordinate is on the line y = mx + c, x and y will be straightforwardly related linearly.
  • The term “linear equation” is given to equations that define straight lines.

Equation of a line Graph

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Solved Example: 

Question 1: How would we get the y value for a given x in the line equation y= 2x – 6?

Solution:

  • Step #1: Analysis y = 2x -6.
  • Step #2: We can find any y-coordinate by inserting a designated x-value into the factored equation, say, x = 2
  • Step #3: Evaluate the required computations by selecting the x-value and finding the prescribed y-coordinate.

If x = 2

y = 2 x 2 – 6

y = 4 – 6

y = -2

Therefore, y equals -2 for the x value which is 2.

Straight Line Answer

Practice Questions

Question 1. How can we find any y-coordinate for a given x value in the line equation y = 3x - 4?

Answer : ( , )


Question 2: How can we find any y-coordinate for a given x value in the line equation y = 5x - 3?

Answer : ( , )

How do you find "m" and "c"?

  • c is easy: see at what point the line crosses the Y-axis.
  • m (the Slope) needs some calculation:

m = Change in Y/ Change in X

How do you find m and c

Equation of line change in y and change in x Formula

How to Find the Equation of a Line

Slope-Intercept Form (y = mx + b):

  • Work out two parameters (slope and y-intercept) from the information provided, e.g. a point on the line or the slope and a point.
  • Plug these values into the slope-intercept form to yield the equation.

Point-Slope Form (y – y1 = m(x – x1)):

  • If you are given the coordinates of a point (x2, y2) on the line along with its slope, you can use the point-slope form to write the equation for it.

Two-Point Form:

  • If you have two particular locations (x1, y1) and (x2, y2) on the line, then to acquire the equation, use the two-point form.

Parallel and Perpendicular Lines:

  • Note that lines with the same slope are parallel, while those with a negative reciprocal slope are perpendicular.
  • Make use of the given information to obtain the equation of a line parallel or perpendicular to a line.
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Conclusion

  • The y = mx + c equation is extremely useful in not only representing but also depicting linear relationships, which is the reason why it is one of the pillars of algebra.
  • Among the various functions it has to fulfil the most significant is visualizing different phenomena, for example, the trajectory of the projectile or the trends in financial data.
  • Its versatility is not limited to a particular field of study and rather furnishes a way to comprehend and convey real-world cases.
  • The equation also provides geometrically the curve of slope and y-intercept which shows important information concerning the line’s relationship.

Worksheet

Question 1: A line has the equation y = 3x + 4. Write down the y-intercept of the line.

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Question 2: Write down where these lines cross the y-axis (y-intercept): y = 2x + 3

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Question 3: Find the coordinates where the following lines cross the x-axis: y = 2x + 6

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Question 4: Find the coordinates where the following lines cross the x-axis: y = -2x + 10

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Question 5: Write down where these lines cross the y-axis (y-intercept): y = 7x + 1

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