Math  /  Algebra

QuestionWHAT IS THE SLOPE OF ALINE A) PARALLEL ANO B) PERPENOICULAR TO EACH OF THE FOLLOWING? 2xy=72 x-y=7 5) PARALLEL SLOPE: \qquad 7) PERPENOICULAR SLOPE: y=25x+9y=\frac{2}{5} x+9 6) PARALLEL SLDPE: \qquad \qquad 8)PERPENDICULAR SLOPE:- \qquad A LINE CONTAINING THE POINTS: P1(7,15)P2(25,15)P_{1}(7,-15) P_{2}(25,-15) 9) PARALLEL SLOPE: \qquad 10) PERPENDICULAR SLOPE: \qquad WRITE THE EQUATION OF A LINE CONTAINING THE FOLLOW ING POINTS 11) P1(2,5);P2(0,9)P_{1}(2,5) ; P_{2}(0,9) 12) P1(8,3);P2(8,32)P_{1}(8,3) ; P_{2}(8,32)
WRITE THE EQUATION OF A LINE WITH THE FOLLOWING INFORMATION 13) m=4ym=4 \quad y-intercept: (0,9)(0,-9) 14) PERPENDICULAR TO: x+3y=5x+3 y=5 AND CONTAIN 15) m=0m=0 point: (1,8)(-1,8) the point (0,6)(0,6)

Studdy Solution

STEP 1

1. A line parallel to another line has the same slope.
2. A line perpendicular to another line has a slope that is the negative reciprocal.
3. The slope-intercept form of a line is y=mx+b y = mx + b , where m m is the slope.
4. The point-slope form of a line is yy1=m(xx1) y - y_1 = m(x - x_1) .

STEP 2

1. Find the slope of the given line 2xy=7 2x - y = 7 .
2. Determine the parallel and perpendicular slopes for the given line.
3. Find the slope of the given line y=25x+9 y = \frac{2}{5}x + 9 .
4. Determine the parallel and perpendicular slopes for the given line.
5. Calculate the slope of the line containing the points P1(7,15) P_1(7, -15) and P2(25,15) P_2(25, -15) .
6. Determine the parallel and perpendicular slopes for the line containing the points.
7. Write the equation of a line containing the points P1(2,5) P_1(2, 5) and P2(0,9) P_2(0, 9) .
8. Write the equation of a line containing the points P1(8,3) P_1(8, 3) and P2(8,32) P_2(8, 32) .
9. Write the equation of a line with a given slope and y-intercept.
10. Determine the slope of a line perpendicular to x+3y=5 x + 3y = 5 and write the equation of the line through a given point.
11. Write the equation of a line with a zero slope through a given point.

STEP 3

Convert the equation 2xy=7 2x - y = 7 to slope-intercept form by solving for y y .
y=2x7 y = 2x - 7
The slope m m of the line is 2 2 .

STEP 4

For a line parallel to 2xy=7 2x - y = 7 , the slope is the same, m=2 m = 2 .
For a line perpendicular to 2xy=7 2x - y = 7 , the slope is the negative reciprocal, m=12 m = -\frac{1}{2} .

STEP 5

The slope of the line y=25x+9 y = \frac{2}{5}x + 9 is 25 \frac{2}{5} .

STEP 6

For a line parallel to y=25x+9 y = \frac{2}{5}x + 9 , the slope is the same, m=25 m = \frac{2}{5} .
For a line perpendicular to y=25x+9 y = \frac{2}{5}x + 9 , the slope is the negative reciprocal, m=52 m = -\frac{5}{2} .

STEP 7

Calculate the slope of the line containing the points P1(7,15) P_1(7, -15) and P2(25,15) P_2(25, -15) .
The slope m m is given by:
m=y2y1x2x1=15(15)257=018=0 m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-15 - (-15)}{25 - 7} = \frac{0}{18} = 0

STEP 8

For a line parallel to the line containing the points, the slope is the same, m=0 m = 0 .
For a line perpendicular to the line containing the points, the slope is undefined (vertical line).

STEP 9

Write the equation of a line containing the points P1(2,5) P_1(2, 5) and P2(0,9) P_2(0, 9) .
Calculate the slope m m :
m=9502=42=2 m = \frac{9 - 5}{0 - 2} = \frac{4}{-2} = -2
Use point-slope form with point (2,5) (2, 5) :
y5=2(x2) y - 5 = -2(x - 2)
Simplify to slope-intercept form:
y=2x+4+5 y = -2x + 4 + 5
y=2x+9 y = -2x + 9

STEP 10

Write the equation of a line containing the points P1(8,3) P_1(8, 3) and P2(8,32) P_2(8, 32) .
The slope is undefined (vertical line), so the equation is:
x=8 x = 8

STEP 11

Write the equation of a line with slope m=4 m = 4 and y-intercept (0,9) (0, -9) .
Use slope-intercept form:
y=4x9 y = 4x - 9

STEP 12

0 Determine the slope of a line perpendicular to x+3y=5 x + 3y = 5 .
Convert to slope-intercept form:
3y=x+5 3y = -x + 5
y=13x+53 y = -\frac{1}{3}x + \frac{5}{3}
The slope of the perpendicular line is the negative reciprocal, m=3 m = 3 .
Write the equation through point (0,6) (0, 6) :
y6=3(x0) y - 6 = 3(x - 0)
Simplify to slope-intercept form:
y=3x+6 y = 3x + 6

STEP 13

1 Write the equation of a line with slope m=0 m = 0 through point (1,8) (-1, 8) .
The equation is horizontal:
y=8 y = 8

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