1.2E: Exercises - Solving Linear Equations in Two Variables

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Jun 27, 2024
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- 1.2: Solving Linear Equations in Two Variables
- 1.3: Determining a Linear Equation

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PROBLEM SET: GRAPHING A LINEAR EQUATION

Work the following problems.

1) Is the point (2, 3) on the line 5x - 2y = 4?

2) Is the point (1, - 2) on the line 6x - y = 4?

3) For the line 3x - y = 12, complete the following ordered pairs.

(2,___) (___, 6)

(0,___) (___, 0)

4) For the line 4x + 3y = 24, complete the following ordered pairs.

(3,___) (___, 4)

(0,___) (___, 0)

Graph the following equations using intercepts.

5) Graph 2x + 4 = 0

6) Graph 2y - 6 = 0

7) Graph the following three equations on the same set of coordinate axes.

$y = x +1 \quad y = 2x + 1 \quad y = -x + 1 \nonumber$

8) Graph the following three equations on the same set of coordinate axes.

$y = 2x +1 \quad y = 2x \quad y = 2x - 1 \nonumber$

Find the slope of the line passing through the following pair of points.

9) (2, 3) and (5, 9)	10) (4, 1) and (2, 5)
11) (- 1, 1) and (1, 3)	12) (4, 3) and (- 1, 3)
13) (3, 4) and (3, 7)	14) (- 2, 4) and (- 3, - 2)
15) (- 3, - 5) and (- 1, - 7)	16) (0, 4) and (3, 0)

Determine the slope of the line from the given equation of the line.

17) y = - 2x + 1	18) y = 3x - 2
19) 2x - y = 6	20) x + 3y = 6
21) 3x - 4y = 12	22) What is the slope of the x-axis? What is the slope of the y-axis?

Graph the line that passes through the given point and has the given slope.

23) (1, 2) and m = - 3/4	24) (2, - 1) and m = 2/3
25) (0, 2) and m = - 2	26) (2, 3) and m = 0

Graph the following equations using their slope and y-intercept.

27) Graph y = 2x + 3	28) Graph y = - 3x + 5
29) Graph y = 4x - 3	30) Graph x - 2y = 8
31) Graph 2x + y = 4	32) Graph 2x - 3y = 6

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PROBLEM SET: GRAPHING A LINEAR EQUATION

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