Write linear equations in point-slope form A1.4.1.2

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[00:00:01]now that we know how to write the equation of a line in slope-intercept form we're going to look at how to use another form called point-slope form point-slope form is y minus y sub 1 equals M times the quantity X minus X sub 1 in this formula the X and the y are not going to change they are going to remain variables but the Y sub 1 the M and the X sub 1 you're going to substitute numbers in for all of those the way that you'll do that is you'll use a point that you're given and the point that you're given will be going in for x1 and y1 so for example if you were given the point 5 comma 6 you would put in the 5 for X sub 1 and you'd put in the 6 for y sub 1 and then the slope will still go in for M after that you will change point-slope form into slope intercept form by distributing the slope across the parenthesis and then solving for y either using addition or subtraction and then after you've completed that step your answer will be in slope intercept form which would look like y equals MX plus B so let's try one we would like to write the equation of the line that goes through the point 6 negative 3 and has a slope of negative 2 so the 6 negative 3 is your point the x1 will be 6 and the y1 will be negative 3 your slope will be your end so we're gonna start with our formula for point-slope form and we're gonna plug in the 3 variables with numbers for the three variables remember that the X and the y are not changing the X sub one we said was 6 the Y sub 1 we said was negative 3 and the M was negative 2 now you might remember from middle school that when you subtract a negative that's the same thing as adding a positive so we're gonna change the Y minus negative 3 into y plus 3 and at this point we now have the equation of a line written in point-slope form what we'll do next is we'll change it into slope-intercept form by making it look like y equals MX plus B by distributing the slope and solving for y so in this question we'll distribute the slope which is negative 2 and we'll come up with y plus 3 equals negative 2x plus 12 and then we'll isolate the Y by using inverse operations and subtracting the 3 3 minus 3 is 0 y plus 0 is y so it's sort of like those threes are cancelling out and then on the other side we have the 12 minus 3 which is 9 so our final answer for this question in slope-intercept form is y equals negative 2x plus 9 let's do one last one here with a fraction this time our point is negative three zero so X sub one is the negative three and zero is the Y sub one and our slope is one third so that's going to be going in for M start with our formula and plug in the three values that we have recall that subtracting a negative is the same thing as adding so we're gonna change this to X plus 3 on the right hand side in the parentheses and on the left remember your identity properties if you add or subtract to see or to something it stays the same so y minus 0 is just Y and this would be our answer in point-slope form and then to change it to slope-intercept form that's where we'll distribute the slope and solve for y so to distribute the slope here we've got 1/3 times X which is 1/3 X and 1/3 times 3 which is 1 and then we actually kind of get to skip this last step because it just happened that our Y sub one was a zero which means we don't need to solve for y y is already isolated