Skip to content# Equation of a line: Graphs, Examples With Worksheet

## What is the Equation of a Line?

### Practice Questions

**Solution:**

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

## How to Find the Equation of a Line

## Conclusion

## Worksheet

**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:

**What is the Equation of a Line?****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

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.

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.

** **

** **

**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.

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

**Step #1:**Examine the line equation y = 3x - 4

**Step #2:**To find any y-coordinate, substitute a specific x value into the equation, for instance, x = 1

**Step #3:**Perform the necessary calculations by substituting the x value and obtaining the corresponding y-coordinate.

If x = 1

**y = 3 x 1 – 4**

**y = 3 – 4**

**y = -1**

For the given x value of 1, the calculated y-coordinate is -1.

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

**Solution:**

**Step #1:**Examine the line equation y = 5x - 3

**Step #2:**To find any y-coordinate, substitute a specific x value into the equation, for instance, x = 2

**Step #3:**Perform the necessary calculations by substituting the x value and obtaining the corresponding y-coordinate.

If x = 2

**y = 5 x 2 – 3**

**y = 10 – 3**

**y = 7**

For the given x value of 2, the calculated y-coordinate is 7.

**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**

**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 – y _{1} = m(x – x_{1})):**

- If you are given the coordinates of a point
**(x**on the line along with its slope, you can use the point-slope form to write the equation for it._{2}, y_{2})

**Two-Point Form:**

- If you have two particular locations
**(x**and_{1}, y_{1})**(x**on the line, then to acquire the equation, use the two-point form._{2}, y_{2})

**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.

- 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.

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

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

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

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

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