Math  /  Geometry

QuestionGraph the linear equation.
1. 2x+y=12 x+y=-1
2. 4xy=64 x-y=6
3. 6x+2y=106 x+2 y=10

Studdy Solution

STEP 1

1. Each equation represents a straight line.
2. We will graph each equation on a coordinate plane.
3. We will find at least two points for each line to ensure accurate graphing.

STEP 2

1. Rewrite each equation in slope-intercept form.
2. Identify the slope and y-intercept.
3. Plot the y-intercept and use the slope to find another point.
4. Draw the line through the points.

STEP 3

For equation 1: 2x+y=12x + y = -1
Rewrite in slope-intercept form (y=mx+by = mx + b):
y=2x1 y = -2x - 1

STEP 4

Identify the slope and y-intercept for equation 1:
Slope (mm) = 2-2, y-intercept (bb) = 1-1

STEP 5

Plot the y-intercept (0,10, -1) on the graph. Use the slope to find another point. From (0,1)(0, -1), move down 2 units and right 1 unit to (1,3)(1, -3).

STEP 6

Draw the line through the points (0,1)(0, -1) and (1,3)(1, -3).

STEP 7

For equation 2: 4xy=64x - y = 6
Rewrite in slope-intercept form:
y=4x6 y = 4x - 6

STEP 8

Identify the slope and y-intercept for equation 2:
Slope (mm) = 44, y-intercept (bb) = 6-6

STEP 9

Plot the y-intercept (0,60, -6) on the graph. Use the slope to find another point. From (0,6)(0, -6), move up 4 units and right 1 unit to (1,2)(1, -2).

STEP 10

Draw the line through the points (0,6)(0, -6) and (1,2)(1, -2).

STEP 11

For equation 3: 6x+2y=106x + 2y = 10
Rewrite in slope-intercept form:
2y=6x+10 2y = -6x + 10 y=3x+5 y = -3x + 5

STEP 12

Identify the slope and y-intercept for equation 3:
Slope (mm) = 3-3, y-intercept (bb) = 55

STEP 13

Plot the y-intercept (0,50, 5) on the graph. Use the slope to find another point. From (0,5)(0, 5), move down 3 units and right 1 unit to (1,2)(1, 2).

STEP 14

Draw the line through the points (0,5)(0, 5) and (1,2)(1, 2).

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