Introduction Straight lines are produced by linear functions. That means that a straight line can be described by an equation that takes the form of the linear equation formula.
Slope-intercept form linear equations Video transcript So you may or may not already know that any linear equation can be written in the form y is equal to mx plus b.
Where m is the slope of the line. The same slope that we've been dealing with the last few videos. The rise over run of the line. Or the inclination of the line.
And b is the y-intercept. I think it's pretty easy to verify that b is a y-intercept. The way you verify that is you substitute x is equal to 0.
If you get x is equal to remember x is equal to 0, that means that's where we're going to intercept at the y-axis.
If x is equal to 0, this equation becomes y is equal to m times 0 plus b. I don't care what m is. So then y is going to be equal to b. So the point 0, b is going to be on that line.
The line will intercept the y-axis at the point y is equal to b. We'll see that with actual numbers in the next few videos.
Just to verify for you that m is really the slope, let's just try some numbers out. We know the point 0, b is on the line. What happens when x is equal to 1? You get y is equal to m times 1. Or it's equal to m plus b.
So we also know that the point 1, m plus b is also on the line. This is just the y value.If a line has no y-intercept, that means it never intersects the y-axis, so it must be parallel to the y-axis.
This means it is a vertical line, such as `x=3`. This slope of this line is undefined. Writing slope-intercept equations. Slope-intercept equation from graph. Writing slope-intercept equations , where this m right over here, that is of the slope of the line.
|Slope-intercept equation from graph (video) | Khan Academy||Let's first quickly review slope intercept form. Equations that are written in slope intercept form are the easiest to graph and easiest to write given the proper information.|
|What is the slope intercept form?||What is the equation of this line in slope-intercept form?|
And this b over here, this is the y-intercept of the line. Let me draw a quick line here just so that we can visualize that a little bit. Slope-intercept equation.
Example 3: Write an equation of the line with y-intercept 3 that is parallel to the line y = 7x - 9. Since y = 7 x - 9 is in slope-intercept form, its slope is 7. Since parallel lines have the same slope, the slope of the new line will also be 7.
A real-life situation of a line that has no y-intercept is the equation of a vertical wall. This is a line such as x=5. A real-life situation of a line that has no x . Straight-line equations, or "linear" equations, graph as straight lines, and have simple variable expressions with no exponents on them.
If you see an equation with only x and y – as opposed to, say x 2 or sqrt (y) – then you're dealing with a straight-line equation. Find the equation of the line that passes through the point (-2, 6) with a slope of 3.