The Equation of Straight Line طرق ايجاد معادلة الخط المستقيم

hello everyone welcome back to easy math five ways to find the equation of straight line mean the equation of straight line in the Cartesian plane how can you find its equation there are really five methods yes let me show you number one slope y-intercept equals MX plus this formula is called slope y-intercept use it when you are given the slope and y-intercept find the equation of straight line whose gradient 3 and intercept negative 2 answer you know right the equation equals MX plus so equal the gradient three plus plus plus plus the point negative 2 that's it thank you you can simplify the equation by writing equals 3x minus 2 that's method number two slope point formula formula if the slope and the point slope of the line and one point on it are given to you to find the equation use this formula please minus equals the into minus it's comes also from the definition of the gradient of line so if you are if you have point one and four over line and this gradient of the line is two was the equation just to write substitute direct here look at this one minus this is and the point 1 and 4 so minus 4 is equal to the slope 2 into minus 1 is equal to 2x minus 2 by using distributive property minus 4 if you really add 4 to each side add 4 here and add 4 here you get 0 here so is equal to 2x plus 2 this is the equation that's very easy slope point formula next one method number three two points formula this is the formula of two points if you have two points given for you to find the equation use this formula direct question and it find the equation of straight line that passes through the point 0 and negative 2 1 & 3 just substitute with these two points here in the formula minus y1 y1 this point consider any point y1 may be this one one one or this one no problem consider now this is x1 y1 and the other point is x2 y2 so minus negative 2 over minus 0 is equal to y2 which 3 minus negative 2 over x2 which is 1 minus 0 so minus negative 2 is plus 2 okay over minus 0 is is equal to 5 over 1 by cross multiplication you know for any proportion if you multiply this means extremes equal the product of means and 5 are the means 1 and plus 2 are the extremes so this implies 1 times plus 2 is plus 2 is equal to 5 times is 5x so equals 5 minus 2 thank you so much that's it okay next one method number four intercept intercept this formula is called x-intercept the y-intercept if you are given the intersection of the line and intersection of the line you can find it easily very easy find the equation of straight line it's an coordinate intercept 3 and intercept is 4 very easy just write over its intercept 3 plus over the intercept 4 is equal to 1 thank you this is very easy you can more simplify this equation put in the general 4 by multiplying all of each side by multiplying each side by 2 by the LCM of 3 & 4 which is 12 just multiplied here by 12 times 12 years times 12 here okay so 12 is divided by 3 4 will be 4x plus 12 is divided by 4 3 3 is equal to have 12 year 1 times this is the equation thank you so much and this is the line this is this equation for this life method here method number five from the graph if you are given the graph of the line can you find its equation yes easy how this question will show you find the equation of the blue and red lines below the equation this line blue parallel to axis and pass through the point three here you know that it's equation equal three and I'd like to show you why equal three here I'd like to show you this equation is equal to three similarly this line this red line it's equation equals two because it passed through the point here tell you now consider the blue line here you know the equation of the line is common property for all points on the line you know this these points if you look at its coordinate this point for example is four and three yes this point three and zero yeah mean the point here is the line three zero and 3 the intercept the other point one and three another point two and three so all points here the coordinate is 3 so the equal 3 becomes the equation of the line because it's common property for all points on this line the same here all points on this line it's intercept to this point is 2 & 1 2 & 2 2 & 3 is 2 and 0 to negative 1/2 negative 2 to negative 3 so all points its x-coordinate is 2 so equal 2 is the equation so easy now to ask you to find this was the equation of this line correct equal negative 3 what's the equation of this line who can tell me yes equals 5 and so on thank you so much you hear find the equation of the blue line this is an oblique line with positive slope want to show you how couldn't find its equation I'm gonna use here the formula equals MX plus is really clear this is this point is - and how can you get the slope of the drawn line go to the drawn line please and assign two exact two points on it like this point and this point don't take this point or this don't take point it's decimal coordinate take exact point and they move from the point to another by this right triangle we are going down one two three three steps down negative three and the two steps left will be negative two so the slope is negative three over negative 2 which is 3 over 2 so the equation simply equals 3 over 2x plus 2 thank you used the and the found it to form the equation okay very easy next one or the last question really have today for with you find the equation of the blue line the same can also use the same method here this is you see here three is equal three there were intercept and the slope go this way and then go this way okay you are going down here negative three because you are moving down and this is really naked positive two goes to the right so the slope is equal to ya this is the slope really is Delta over Delta Delta means change in over change if for for any two points the two points already assigned them it's very important assign the two points first and then move from the one point to another so it's negative 3 over 2 so the equation equals negative 3 over 2 plus 3 okay thank you for watching this video today and hope you do subscribe if you see these videos useful for you or helpful and share to anyone need these information from your friends thank you goodbye you