How To Find The Slope Of A Line?

how to find the slope of a line

In Algebra and Geometry, if you know how to find the slope of a line you are sorted! The term slope is used to describe the steepness and direction of lines in maths. You can easily determine the slope of a line from its graph by looking at the rise and run. In today’s post, I will focus on how to find the slope of a line equation. It is the difference between the y-coordinates of 2 points divided by the difference between the x-coordinates of 2 points. Without wasting much time, let us now check out how to find the slope of a line in more detail.

How To Find The Slope Of A Line?

In this section, I will teach you how to find the slope of a line. To determine this value, you need to understand the concept of rise and run. Some people call the y-coordinates the rise and the x-coordinates the run.

Follow these steps to know how to find the slope of a line on a graph.

  1. First, recall the slope formula which is: m = y2 – y1 / x2 – x1.
  2. Now, look at the line on the graph whose slope you want to calculate.
  3. Check through which two coordinates the line passes.
  4. Then, pick which point’s coordinates are dominant in your equation.
  5. Name the dominate coordinates x1 and y1.
  6. Now, the other two coordinates will be x2 and y2.
  7. Substitute the values of x and y coordinates in the slope equation.
  8. Solve this slope equation to get the value of m.

The final answer you get will be the slope of a straight line. You can also cross-check the value if it’s correct by looking at the line graph.

You can now keep on reading to know more about how to find the slope of a line graph.

Find The Slope Of A Perpendicular Line

A slope of a perpendicular line is the product of the slope of individual lines. You can follow these steps to know how to find the slope of a perpendicular line.

  1. First, recall the formula of the slope of a perpendicular line which is: m1.m2 = -1.
  2. Here, m1 and m2 are the slopes of the individual lines.
  3. Take the general form of the equation of one of the perpendicular lines.
  4. This can be ax + by + c = 0.
  5. Here, x and y are the coordinates of the line, and c is some constant.
  6. Convert this equation into the slope-intercept form which is y = -ax/b -c/b.
  7. Substitute these values to get the slope of a perpendicular line m1.
  8. Here, the value of m1 will be -a/b.
  9. Put this m1 value in the slope formula m1.m2 =-1.
  10. Now, find the slope of the other perpendicular line which is m2=b/a.

That’s how you can get the value of the slope of a perpendicular line. Make sure you don’t skip any step or else you’ll end up with the wrong answer!

Find The Slope Of A Parallel Line

Parallel lines are those lines that never intersect with each other. The slopes of both the parallel lines are the same. You can follow these steps to know how to find the slope of a parallel line.

  1. Recall the point-slope equation which is y – y1 = m1(x – x1).
  2. Here, (x, x1) are x-coordinates, and (y, y1) are y coordinates.
  3. Now, look at the line on the graph whose slope you want to calculate.
  4. Check through which two coordinates the line passes.
  5. Then, pick which point’s coordinates are dominant in your equation.
  6. Name the dominate coordinates x1 and y1.
  7. Now, the other two coordinates will be x2 and y2.
  8. Substitute the values of x and y coordinates in the slope equation.
  9. Solve this slope equation to get the value of m1.
  10. You can repeat the same procedure to find the slope of another parallel line m2.

If the values of m1 and m2 are the same, the value of m you’ve calculated is correct. However, you can even use this formula m = y2 – y1 / x2 – x1 to find the value of m1 and m2.

Find The Slope Of A Tangent Line

A tangent line is basically a straight line that just touches the curve at a certain point. You can follow these steps to know how to find the slope of a tangent line.

  1. First, recall the slope of a tangent line formula which is: y – y⁠⁠⁠⁠⁠⁠⁠1 = m × (x – x⁠⁠⁠⁠⁠⁠⁠1 ) or y= mx + c.
  2. Here, x and y are the coordinate points, m is the slope, and c is some constant.
  3. Now, look at the line on the graph whose slope you want to calculate.
  4. Check through which two coordinates the line passes.
  5. Then, pick which point’s coordinates are dominant in your equation.
  6. Name the dominate coordinates x1 and y1.
  7. Now, the other two coordinates will be x2 and y2.
  8. Substitute the values of c, x, and y coordinates in the slope equation.
  9. Solve this slope equation to get the value of m.

Using this slope of the tangent line formula, you can also find the equation of the tangent line. 

Find The Slope Of A Line Without Points

Do you know how to find the slope of a line without points? Unfortunately, you cannot find the slope of a line without points. If a line equation is given to you, you can compare it with the straight line equation y = mx + b. Simply substitute the values of y, x, and b to get the slope of a line m.

Read more about different topics on Fyndblog

FAQ

How Do You Calculate Slope Of Line?

Pick two points on the line and determine their coordinates. Determine the difference in y-coordinates of these two points (rise). Determine the difference in x-coordinates for these two points (run). Divide the difference in y-coordinates by the difference in x-coordinates (rise/run or slope).

How Do I Find Slope With Two Points?

Use the slope formula to find the slope of a line given the coordinates of two points on the line. The slope formula is m=(y2-y1)/(x2-x1), or the change in the y values over the change in the x values. The coordinates of the first point represent x1 and y1. The coordinates of the second points are x2, y2.

How Do I Find Slope And Y-Intercept?

Solutions. The equation of the line is written in the slope-intercept form, which is: y = mx + b, where m represents the slope and b represents the y-intercept. In our equation, y = 6x + 2, we see that the slope of the line is 6.

What Is Slope In Straight Line?

Generally, the slope of a line gives the measure of its steepness and direction. The slope of a straight line between two points says (x1,y1) and (x2,y2) can be easily determined by finding the difference between the coordinates of the points. The slope is usually represented by the letter ‘m’.

Conclusion

In the above post, I’ve explained how to find the slope of a line with two points in detail. This task can be pretty easy if you understand the slope formula first. It is defined as rise over run! In general, it is m = y2 – y1 / x2 – x1. Enter the y coordinates on the top and the x coordinates at the bottom. Now, subtract the two y coordinates and the two x coordinates. Remember that you can’t find the slope of a line that isn’t straight. By understanding how to find the slope of a line, you can easily get the value of m!

 

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