Slope-intercept form linear equations Standard form linear equations Point-slope form linear equations Video transcript A line passes through the points negative 3, 6 and 6, 0. Find the equation of this line in point slope form, slope intercept form, standard form. And the way to think about these, these are just three different ways of writing the same equation.
You could write it in slope-intercept form, where it would be of the form of Y is equal to MX plus B, where M and B are constants. M is the coefficient on this MX term right over here and M would represent the slope.
Literally the graph that represents the XY pairs that satisfy this equation, it would intersect the y-axis at the point X equals zero, Y is equal to B. So let me make it clear. And these are just different ways of writing the same equations.
You can algebraically manipulate from one to the other. Another way is point-slope. Slope is equal to M. This is point-slope form and we do videos on that. But what I really want to get into in this video is another form.
And that is standard form. And we wanted to graph this. So how do we do that? And the y-intercept is going to happen when X is equal to zero. So when Y is zero, what is X? So if nine times X is 72, 72 divided by nine is eight. So X would be equal to eight. So once again, that was pretty easy to figure out.
This term goes away and you just have to say hey, nine times X is 72, X would be eight. When Y is equal to zero, X is eight. This point right over here is the x-intercept. Now what about the y-intercept?
Well, we said X equals zero, this disappears. And so we could solve, we could solve that.
So we could say, alright 16Y is equal to Writing linear equations using the slope-intercept form Writing linear equations using the point-slope form and the standard form Parallel and perpendicular lines.
Find the slope of any line perpendicular to the line through the points (0,5) and (-3,-4) Write the equation of the line passing through each of the given pairs of points.
Write the answer in slope-intercept form, where possible. 2. Write the equation in slope-intercept form. Identify the slope and y-intercept.
SHOW ALL WORK x - 4y = Write an equation for the line in point-slope form. (2 points) b. Rewrite the equation in standard form using integers.
(2 points)5/5(7). Given the graph of a line, you can determine the equation in two ways, using slope-intercept form, y = m x + b, or point-slope form, y − y 1 = m (x − x 1). The slope and one point on the line is all that is needed to write the equation of a line.
y = mx + c is the standard equation for a line. Where, m is the gradient of the slope c is the intersection of the graph with the y-axis y is any y co-ordinate on the line x is any x co-ordinate on the line To find the gradient we use the formula.
To start transforming the equation we wrote to standard form we can add #color(red)(6)# and subtract #color(blue)(1x)# from each side of the equation to put both variables on the left side of the equation and the constant on the right side of the equation.