Write an equation for each line described. Give answers in standard form for Exercises 11–20 and in slope-intercept form (if possible) for Exercises 21–32. x-intercept (3,0), y-intercept (0,-2)

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Accepted Answer

Welcome back. I am so glad you're here. We are asked to find the equation of a line having an X intercept and A Y intercept equal to 50 and zero negative four respectively. Were to write the equation in slope intercept form. All right. Well, we recall from previous lessons, slope intercept form is the format of Y equals M X plus B where M is our slope and B is our Y intercept. And what do we have in our given practice problem? We do have the Y intercept that is zero negative four. And we recall from previous lessons that when we're given this in a point that is zero comma B where B is that value and here B is negative for then we also need the slope, but we don't have the slope. We're not given the slope in this one. So what do we do? Well, we are given two points and we recall from previous lessons that when we have two points, we can use those two points to figure out the slope. We use the formula in the numerator Y two minus Y one divided by in the denominator X two minus X one. So where are exes and wise and all those things? Well, we can bring down this 50 and 50. That can be because it's our first point. That can be our X one and R Y one, Then we can bring down the 0 -4 And that can give us our X two and our Y two. And so we can plug those back into our equation in the numerator is starting with Y two, that would be negative four minus and then Ry one, that's zero over our X two, that's zero minus R X one, that's five. So in the numerator that simplifies negative four minus zero is negative four. And in the denominator zero minus five is negative five and a negative divided by a negative, those are going to be positive. So we have 4/5 and that's our slope. So now we've got our slope and our Y intercept and we can plug those in to our equation for slope intercept form. So we have Y equals M our slope. That's 4/5 X plus B R Y intercept. That's negative four. We can do one bit of simplifying here. We can bring this down, Y equals 4/5 X and then plus negative four, that's just minus four. So here's our equation in slope intercept form. We look at our answer choices for Y equals 4/5 X. If we multiplied the four in the X together, that would be four X over five. So that's the same thing. So Y equals 4/5 X or four X over five minus four. And that matches with answer choice. A well done. We'll catch you on the next one.

Write an equation for each line described. Give answers in standard form for Exercises 11–20 and in slope-intercept form (if possible) for Exercises 21–32. x-intercept (3,0), y-intercept (0,-2)

Verified Solution

Key Concepts

Intercepts

Slope-Intercept Form

Standard Form of a Linear Equation