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Math  /  Algebra

QuestionName: Ayda Avila 0.
Writing Systems of Equations Mixed Practice
1. Write a system of equations to represent the following graph. A. 4x+9y=364 x+9 y=36 C. 4x+9y=364 x+9 y=36 y=3x−2y=3 x-2 6x−2y=−46 x-2 y=-4 B. 9x+4y=369 x+4 y=36 D. y=3x−2y=3 x-2 y=−3x−2y=-3 x-2 y=−94x+4y=-\frac{9}{4} x+4

Studdy Solution

STEP 1

1. We are given a graph with two intersecting lines.
2. We need to write a system of equations that represents these lines.
3. The equations of the lines can be determined using the slope-intercept form y=mx+b y = mx + b .

STEP 2

1. Determine the equation of the first line using the points (0, -2) and (1, 1).
2. Determine the equation of the second line using the points (0, 4) and (4, -5).
3. Identify the correct system of equations from the given options.

STEP 3

Find the slope m m of the first line using the points (0, -2) and (1, 1).
m=1−(−2)1−0=31=3 m = \frac{1 - (-2)}{1 - 0} = \frac{3}{1} = 3
The equation of the line in slope-intercept form is:
y=3x−2 y = 3x - 2

STEP 4

Find the slope m m of the second line using the points (0, 4) and (4, -5).
m=−5−44−0=−94 m = \frac{-5 - 4}{4 - 0} = \frac{-9}{4}
The equation of the line in slope-intercept form is:
y=−94x+4 y = -\frac{9}{4}x + 4

STEP 5

Identify the correct system of equations from the given options:
From STEP_1 and STEP_2, the equations are:
1. y=3x−2 y = 3x - 2
2. y=−94x+4 y = -\frac{9}{4}x + 4
Option D matches these equations:
y=3x−2 y = 3x - 2 y=−3x−2 y = -3x - 2 (Note: This is incorrect, should be y=−94x+4 y = -\frac{9}{4}x + 4 )
Upon reviewing, none of the given options perfectly match the derived equations. However, option D is closest with one correct equation.

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