For each line, (a) find the slope and (b) sketch the graph. y ...

Question

For each line, (a) find the slope and (b) sketch the graph. y = 2x - 4

Accepted Answer

Hello everybody. I hope everything right today, today, we're going to be looking at this question that states determine the slope for the given line and plot it on the rectangular coordinate system where the equation for our line is Y equals 18 X minus three. Now, when looking at an equation like this, I see that it is in written in a way that we call slope intercept form. And now we have to think what is slope intercept form? Well, slope inter intercept form is written generally as Y equals M X plus B where M is equal to slope and B is equal to the Y intercept. So now we move our equation and try to work with it and see what each of our slope and our would be. So again, we had Y equals 18 X minus three. So our M here is equal to 18 and R B here is equal to negative three or a point for the Y intercept at zero, comma negative three. And just like that, just from looking at the equation, we already have obtained our slope and one point our Y intercept. No, for our X intercept all we have to do is plug in zero for the Why? So we had Y equals 18 X minus three. And if we plug in zero for Y, we'll have that zero is equal to 18 X minus three. So now we move the three over from the right hand side to the left hand side and we do that by adding, so we have three is equal to 18 X. And now to isolate the X, we divide both sides by 18. So we'll have three, divided by 18 is equal to X. And we can simplify this further by dividing both the numerator and the denominator by three to have one divided by six equals X or a point at one divided by six comma zero. And that will be our X intercept. So now we have our slope and two points that we can connect. And with that information, we can go ahead and go draw a general idea of what the graph will look like. So for that, I wanna draw a Y axis and an X axis and will drop a point at negative three. So we draw a couple lines for negative one, negative two and negative three at the Y. And we'll do the same thing as positive, we'll have 12 and three. And now we can plug in the point at zero comma negative three, which was our Y intercept. And for our X intercept, I will draw in some dashes for positive one, positive two and positive three. And we know that we intersect at one divided by six, which is a bit less than half. So I try to measure it between zero and one. I see where the half is around uh I estimate where half is and go a little bit less than that. And that's where I'll connect my point and I just connect the two points simply and continue the line upwards and downwards and labeled both of my points. So we had one at zero, comma negative three and one at one divided by six comma zero. And just like that, we obtained our slope, our Y intercept and our X intersect. And we were able to draw a general idea of what our line should look like in a rectangular recording system. So I hope that was helpful. And until next time.

For each line, (a) find the slope and (b) sketch the graph. y = 2x - 4

Key Concepts

Slope of a Line

Slope-Intercept Form of a Line

Graphing Linear Equations

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