Solve each system for x and y, expressing either value in term...

Question

Solve each system for x and y, expressing either value in terms of a or b, if necessary. Assume that a ≠ 0 and b ≠ 0. For the linear function f(x) = mx + b, f(−2) = 11 and ƒ(3) = -9. Find m and b.

Accepted Answer

Welcome back. I am so glad you're here. We are given several functions were given F of two equals eight, and f of six equals negative four. And told that these are for the linear function F of X equals M X plus B. And our job is to solve for M the slope and B. The Y intercept. Okay, now we can identify our F. Of X and R X from these two functions on the left hand side. If we've got F of X equals M X plus B. The X value is here inside the parentheses. So the X value will go right here and we don't know our M. And we don't know our B yet. And our F of X. Well, that's what this whole thing is equal to its equal to eight. So the left hand side will be eight. We can do the same matching up for our F of six equals negative four. So our X value, let's put that here. Again, A five X equals M X plus b. R X value is going to be inside the parentheses. So that will go here where the X. Is. We don't know R. M or r. B. That's what we're solving for. And our F of X. That is equal to this whole thing here, that is -4. So now we have a system of equations and we can solve for M&B. Using our system of equations. Well, I'm going to set both of these equations equal to B and then we can set them both equal to each other. So I'm going to subtract, This is six M. That's how we more traditionally see it And this one is to em from both sides. So now this equation reads -2 m equals b. And this equation reads negative four minus six M equals B. And since they both equal B, they both equal each other. So now we can solve here for em, let's bring our M values to the right hand side, will add to em to both sides and then add four to both sides, bringing the constant terms over to the left. So eight plus four equals 12 on the left hand side and negative six. M plus two. M equals negative four M. On the right hand side, Dividing both sides by -4. We've got 12 divided by negative four while M equals a negative three. So we've solved for our slope for our m Great. Now we can go back to any of these original equations and we can substitute in for M and solve for B. So let's use this equation here. So we've got negative four equals now M is negative three times six plus B. Negative four equals negative three times six is negative 18 plus B. We can add 18 to both sides. And we get a solution of b equals positive 14. So we've got M equals negative three and B equals 14. We look at our answer choices. And this matches with answer choice C. Well done. We'll catch you on the next one.

Solve each system for x and y, expressing either value in terms of a or b, if necessary. Assume that a ≠ 0 and b ≠ 0. For the linear function f(x) = mx + b, f(−2) = 11 and ƒ(3) = -9. Find m and b.

Key Concepts

Linear Functions

Slope of a Line

Solving Systems of Equations

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