# How to write an equation of the line shown

## How to find the equation of a line on a graph

Incidentally I can also write eleven-halves as 5. And so that will put me at 5,4. We wanna get a little closer to that point 7,Q. So that would mainly move the x goes up by 3, so it goes from -2 to positive 1. Of course- five-thirds times 2 is positive ten-thirds. We have a slope of- five-thirds, and we get a point on the line -2, 7 and we wanna know what is the x-intercept of the line. I have the equation of line J. Now that you understand the slope-intercept form, you can look at the graph of a line and write its equation just by identifying the slope and the y-intercept from the graph. The bar labeled b changes the y-intercept. And it must be true that rise over run, h over 2, equals the slope of the line. When working with linear relationships, the slope-intercept form helps to translate between the graph of a line and the equation of a line. So that is a graphical way of solving the exact same question again. Plug the slope in, we can solve for b, and then we have full slope intercept form. The slope is primary information about the line.

So we set up this proportion. And the slope well, since it goes to -2, we have a run of 2, and a rise of 1, so rise over run would be one-half.

## Slope calculator

Three-halves, I can write that as 1. Algebraic Solution Well again we have a couple of ways to think about this. Again that is a perfectly valid way to solve the problem. The bar labeled b changes the y-intercept. Find the value of Q. We have a rise of 3 and a run of 4. If we wanna get closer to the y-intercept, because it has a negative the x intercept, we need to move to the right, because it has a negative slope. Graphical Solution Algebraic solutions will always get you to an answer. We find a common denominator and then we subtract and we get the y-intercept. So again you have to find the slope. So rise over run is three-fourths. And so we could move with a run of 3, and then drop the height by Well we have two very different ways of going about this. The first is what I would call an algebraic solution.

Now, what we need to find is the x-intercept. Plug the slope in, we can solve for b, and then we have full slope intercept form.

### How to write an equation of the line shown

Now we can figure out the height of Q. We have a slope of- five-thirds, and we get a point on the line -2, 7 and we wanna know what is the x-intercept of the line. Simply by changing the values of m and b, you can define any line. Well we have two very different ways of going about this. And then b would be 7- ten-thirds. I also wanted to show a completely different way of thinking about this problem, what I would call a graphical solution. We have a rise of 3 and a run of 4. When working with linear relationships, the slope-intercept form helps to translate between the graph of a line and the equation of a line.

So in other words, if we just look at the absolute values 2 over b. We have a slope of- five-thirds, and we get a point on the line -2, 7 and we wanna know what is the x-intercept of the line. Another Way to Solve That will get the answer.

Another question, solving for the equation of the line will be very helpful in finding what the question asks. So that is a graphical way of approaching this. And then just solve for b. And the y goes down by 5 so it goes from 7 down to 2.

We go through the point -3,-3we go through the point 1,1. Algebraic Solution Well again we have a couple of ways to think about this.

So the bottom of the slope triangle of this diagram is at a height of 4. The bar labeled b changes the y-intercept.

### Finding the equation of a line given two points

We wanna get a little closer to that point 7,Q. The bar labeled m lets you adjust the slope, or steepness, of the line. So again you have to find the slope. The first is what I would call an algebraic solution. But I would point out if you can solve the problem algebraically and also solve it graphically using proportions, then you really understand it very deeply. And it must be true that rise over run, h over 2, equals the slope of the line. Well that allows us to solve for that little b there. And again, if you can solve the problem both ways with an algebraic solution and a graphic solution you understand this topic extremely well. Okay, line J passes through the points -3, -2 , 1,1 , and 7,Q. And notice that little triangle that we make there, that has to be a slope triangle. We want the x-intercept. Practice Problem Once you have the slope, you may able to think about the question graphically as well. And remember, you often have the option of solving algebraically or graphically thinking about the proportions involved for the slope.

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