Math  /  Algebra

QuestionGrade:
What Happened When Two Fruit Companies Merged? For each exercise below, find the equation of the line passing through the given points. Circle the two letters next to the correct equation. Then write these letters in the two boxes at the bottom of the page that contain the number of that exercise. (1) (1,5)(2,7)(1,5)(2,7) (2) (0,1)(3,8)(0,1)(3,-8) (3) (2,3)(4,2)(2,-3)(4,-2) (4) (2,5)(4,2)(2,5)(4,2) (5) (3,5)(1,3)(-3,-5)(-1,3) (6) (3,1)(6,4)(3,-1)(-6,-4) (7) (4,1)(4,7)(4,1)(-4,7) (8) (1,2)(3,4)(-1,2)(3,4) (9) (1,4)(2,0)(-1,-4)(2,0) (10) (3,1)(3,5)(3,-1)(-3,5)
Answers: 151-5 (IS) y=23x+3y=\frac{2}{3} x+3 (TH) y=12x4y=\frac{1}{2} x-4 (AP) y=32x+8y=-\frac{3}{2} x+8 (II) y=3x+5y=-3 x+5 (ST) y=12x7y=\frac{1}{2} x-7 (DE) y=2x+3y=2 x+3 (CT) y=3x+1y=-3 x+1 (EY) y=4x+7y=4 x+7 (LO) y=32x4y=-\frac{3}{2} x-4 (II) y=2x+1y=2 x+1 (ER y=34x+4y=-\frac{3}{4} x+4 (EL) y=2x1y=-2 x-1 (EA) y=34x+2y=-\frac{3}{4} x+2 (AR y=13x2y=\frac{1}{3} x-2 (FE) y=43x83y=\frac{4}{3} x-\frac{8}{3}

Studdy Solution

STEP 1

What is this asking? We need to find the equation of a line that goes through two given points for each exercise, and then match it with the correct equation from the answer list! Watch out! Don't mix up the xx and yy coordinates, and be careful with negative signs during calculations.

STEP 2

1. Find Slope
2. Find Intercept
3. Match Equation

STEP 3

Let's **start with exercise (1)**, with points (1,5)(1, 5) and (2,7)(2, 7).
Remember, the **slope** is the change in yy over the change in xx.
We can write this as: m=y2y1x2x1 m = \frac{y_2 - y_1}{x_2 - x_1}

STEP 4

Plugging in our **values**, we get: m=7521=21=2 m = \frac{7 - 5}{2 - 1} = \frac{2}{1} = 2 So our **slope** is 22!

STEP 5

Now we need to find the **y-intercept** (where the line crosses the y-axis).
We can use the **point-slope form** of a line: yy1=m(xx1) y - y_1 = m(x - x_1)

STEP 6

Let's use the **first point** (1,5)(1, 5) and our **slope** m=2m = 2: y5=2(x1) y - 5 = 2(x - 1)

STEP 7

**Distribute** the 2: y5=2x2 y - 5 = 2x - 2

STEP 8

**Add** 55 to both sides to **isolate** yy: y=2x2+5 y = 2x - 2 + 5 y=2x+3 y = 2x + 3

STEP 9

Our equation is y=2x+3y = 2x + 3.
Looking at the answers, this matches with **(DE)**!
We'll do this same process for the rest of the exercises.

STEP 10

We'll follow the same **slope-intercept method** for the remaining exercises.
The detailed calculations are left as an exercise for the viewer, but here's a summary of the results:
(2) y=3x+1y = -3x + 1 **(CT)** (3) y=12x4y = \frac{1}{2}x - 4 **(TH)** (4) y=32x+8y = -\frac{3}{2}x + 8 **(AP)** (5) y=4x+7y = 4x + 7 **(EY)** (6) y=13x2y = \frac{1}{3}x - 2 **(AR)** (7) y=34x+4y = -\frac{3}{4}x + 4 **(ER)** (8) y=12x+52y = \frac{1}{2}x + \frac{5}{2} (Not listed, double check calculations!) (9) y=43x83y = \frac{4}{3}x - \frac{8}{3} **(FE)** (10) y=x+2y = -x + 2 (Not listed, double check calculations!)

STEP 11

(1) DE (2) CT (3) TH (4) AP (5) EY (6) AR (7) ER (8) Double check calculations! (9) FE (10) Double check calculations!

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