How to find the equation of a line given one point and a slope
Guess what, I am not a Math student and when I was a kid and during my teenage years. I love math but it was my biggest nightmare and the most difficult subject I was taught. I am an adult now and every day even though the subject is hard, I keep improving day after day because I want to learn and this was also necessitated by the fact I study Information Technology and so I have to do deal with computer architecture and some maths. So as the title of this post goes by, I am going to teach you how to determine and find the equation of a line given or passing through one point
Example 1: -
Let's find the equation of the line with a gradient or slope as it is generally regarded of 4 passing through a given point (3, -2)
Rule Number 1:
When solving problems in relation to slope, you have to apply the law of BODMAS sign result which is as follows
When multiplying numbers:
positive × positive = positive
negative × negative = positive
positive × negative = negative
negative × positive = negative
Rule Number 2:
When given a point for example(3, -2), always remember that the first value represent x1 and that is 3 while the second represent y1 which is 2 and so we have (x, y).
The general formula for solving this type of problem is given as
y - y1 / x - x1 = m or
y - y1
-------- = m (gradient or slope)
x - x1
And the final equation has to be in form of a straight line which is y = mx + c
So going by the general formula, you should have
y - (-2)
--------- = 4/1 (there is an invisible one for every integer or whole number)
x - 3
= y + 2 (remember -(-2) implies -1 * -2 = 2 and so there is an invisible value of 1)
-------- = 4/1
x - 3
What you are going to do next is applying the law of cross multiplication and so you have the output as
1(y + 2) = 4(x - 3) which is also equal to
1y or y + 2 = 4x - 12
and so applying the rule of transposition and formulae, we have to subtract both side by 2 which will give us y + 2 - 2 = 4x - 12 - 2 and the final output and answer is
y = 4x - 14 because 2 - 2 = 0 and also -12 + -2 = -14
Example 1: -
Let's find the equation of the line with a gradient or slope as it is generally regarded of 4 passing through a given point (3, -2)
Rule Number 1:
When solving problems in relation to slope, you have to apply the law of BODMAS sign result which is as follows
When multiplying numbers:
positive × positive = positive
negative × negative = positive
positive × negative = negative
negative × positive = negative
Rule Number 2:
When given a point for example(3, -2), always remember that the first value represent x1 and that is 3 while the second represent y1 which is 2 and so we have (x, y).
The general formula for solving this type of problem is given as
y - y1 / x - x1 = m or
y - y1
-------- = m (gradient or slope)
x - x1
And the final equation has to be in form of a straight line which is y = mx + c
So going by the general formula, you should have
y - (-2)
--------- = 4/1 (there is an invisible one for every integer or whole number)
x - 3
= y + 2 (remember -(-2) implies -1 * -2 = 2 and so there is an invisible value of 1)
-------- = 4/1
x - 3
What you are going to do next is applying the law of cross multiplication and so you have the output as
1(y + 2) = 4(x - 3) which is also equal to
1y or y + 2 = 4x - 12
and so applying the rule of transposition and formulae, we have to subtract both side by 2 which will give us y + 2 - 2 = 4x - 12 - 2 and the final output and answer is
y = 4x - 14 because 2 - 2 = 0 and also -12 + -2 = -14