The graph of a linear function f is shown. (a) Identify the slope...

Question

The graph of a linear function f is shown. (a) Identify the slope, y-intercept, and x-intercept. (b) Write an equation that defines f.

Accepted Answer

Hello everybody. I hope you're doing. All right. Today, we're going to be looking at this math question that states determine the X intercept Y intercept and the slope of the line whose graph is shown also write a linear function F that represents the line. Now, the XS provided are A X intercept at negative eight divided by five Y intercept at 200 slope of 80. And a function F of X is equal to 80 X plus 200 B X intercept at negative A divided by three, the same Y intercept as a, the same slope as A and the same function as A B, the same intercept X intercept as a, the same Y intercept as a, the A slope of 75. And a function of F of X is equal to 75 X plus and D, the same X intercept as B, the same Y intercept as A B and C, the same slope as C and the same function as C No. To go further into this question, I have to look at the graph that they provided us. So I see the graph has a positive slope and it passes through two points clearly shown. So it passes through the 0.0 comma and another point on the third quadrant negative four comma negative 100. So those are two points that I will be working with throughout this problem. So first, I can use these two points to find the slope of our line because the slope equation where is M I meaning so is equal to Y two minus Y one in the numerator of a fraction divided by X two minus X one. And for those variables, we just plug in the point that we have. So we would have negative 100 minus 200 on the numerator. And the denominator would be negative four minus zero. And that will simplify to negative divided by negative four, which is equal to 75. So or slope M equals 75. And that will be our first answer here. And right away, we can eliminate answer choices a and being because they have a different slope. So now I'm going to use something called point slope form and I'll write it here. So point slope four and that is Y minus Y one is equal to m multiplying an open parentheses, X minus X one, closed parentheses. And once again, now we just pick one of the points and plug their information in. So I'm going to be using the 0.0 comma 200. So I have Y minus and that Y one will be the 200. So Y minus 200 equals the slope which we obtained, which was 75 multiplying X minus the X one, which here is zero. Now, we can distribute and it will be Y minus 200 is equal to 75 multiplied by X which is 75 X and then 75 multiplied by zero, which is just zero. So we'll have Y minus 200 equals 75. So, or 75 X, so then we'll have Y is equal to 70 X plus 200. And they want this as a function. So all we have to do is replace the Y for F of X. So we'll have that F of X, it's equal to 75 X plus 200. And that'll be the function four, our line. No, I can continue and look at the X intercept. And we should note that the Y intercept was already obtained. And we can just look at that by the, uh at the graph. So the graph intersects the Y access at zero comma 200. So the wine intercept was already given to us within that graph. So lastly, we look at the X intercept. Now for the X intercept, we have to know that all we have to do is plug in zero for our Y. So we use the same formula that our line formula. So which was Y equals 75 X plus 200. And now we just plug in zero for the Y. So we have zero is equal to 75 X plus 200. And then we can simplify it to have 75 X is equal to negative 200. So what we did was move the 200 over. And then if we divide both sides by 75 we'll have that X is equal to negative 200 divided by 75. And we can simplify this further. If we divide both the numerator and the denominator by 25 we'll have that X is equal to negative eight divided by three. And that will be our intercept. So now we have a Y intercept of 200 a slope of 75. A function of F of X equals 75 X plus 200 an X intercept of negative eight divided by three. And all those values match up with answer choice D so I hope that was helpful. And until next time.

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The graph of a linear function f is shown. (a) Identify the slope, y-intercept, and x-intercept. (b) Write an equation that defines f.