Find the equation of the line that intersects the lines 2x + y – 1= 0 = x – 2y + 3z 3x – y + z + 2 = 0 = 4x + 5y – 2z – 3 and is parallel to the line 1 23

Q: Find the intersection point of the line 3x – 2y = 0 and the line passing through (-1, 0) and…

A: equation of one line 3x-2y=0 And second line passing through (-1,0) and is vertical (perpendicular)…

Q: Q10)The two lines L1: x=3-2t, y=4+t ,z= 6-t and L2: x=5-4t, .y=-2+2t, z=7-2t are parallel

A: 10) The equation of the line x=3-2t t=x-3-2 y=4+t t=y-4 z=6-t t=z-6-1

Q: Find the equation of the line that passes through the point (-1, 3) and is parallel to the line 5x –…

A: Two parallel lines have the same slope.   The slope-intercept form of a line is given by:…

Q: Find the equation of line thru P: (1, -2,1) perpendicular to z= 2x – 3y + 7

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Q: 2. Find the equation of the line (a). Through (1,3) with m = -2; (b). x-intercept -2, y-intercept 4;…

A: we know that equation of line is :  y - y1 = m ( x - x1 )

Q: 5. Find the equation of the line perpendicular to 3x - 2y = 5 that goes through the point (3, -4). O…

A: Please refer the attached image for complete solution.

Q: Find an equation of the line that satisfies the given conditions. Through  (1, −1);   parallel to…

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Q: raction of the lines 3y - x=2, 2y-5x

A: Given:- 3y - x=2, 2y-5x=7  and  y - 2x=7 To find the equation of the line passing through the point…

Q: Q2): Find the equation of the line passes through p(2,-4,5), normal to 971. x+8 = 2t, y-5= 3t, 1 -z…

A: Given problem:- Find the equation of the line passes through p(2,-4,5), normal to x + 8 = 2t, y - 5…

Q: prove that the equation 2x²+3xy-2y²-x+3y-1=0 represents a pair of perpendicular lines

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Q: Suppose the symmetric equations of lines l1 and l2 are = 2 – y = z and x = -1, 2 3 espectively.

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Q: Sketch the lines 3x+ 4y 7 and x- 2y = 6, and find their point of intersection. Hint: Their point of…

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Q: Find the equation of the line containing the point (6, 1) and perpendicular to the line y=-5x+2. O…

A: Solve by slope form of line

Q: Find the point of intersection of the lines with the given equations. 6x + 4y = −10   and   6x + 9y…

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Q: Find the point of intersection of the lines with equations x + 4y = 11 and 2x + 5y = 16

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Q: Prove that the equation 2x²+3xy - 2y-x+3y -1= 0 represents a pair of perpendicular lines.

A: Given that: 2x2+3xy-2y2-x+3y-1=0

Q: Find the equation of the line parallel to 8x +4y = 1 passing through the point (0, 1). %3D

A: Given equation is 8x+4y=1 We have to find the equation of line parallel to 8x+4y=1 passing through…

Q: Find the equation of the line containing the point (6, 1) and perpendicular to the line y =-5x+2. 1…

A: Answer is mentioned below

Q: parallel

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Q: 6.) Find the equation of the line perpendicular to 2y – 8x = 24 which also passes through the point…

A: Concept : The product of the slope of the two perpendicular line is -1 Given, the equation of the…

Q: Q1/ Find the equation of a line passing through (1,2) orthogonal to the line passing through (2,…

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Q: Find the equation of the line passing through the point (2, 1) and that is perpendicular to the line…

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Q: Find an equation for the line L that contains the point the point P = (−2, 4, 1) and is orthogonal…

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Q: prove that the equation 2x2+3xy-2y2-x+3y-1=0 represents a pair of perpendicular lines

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Q: Write the equation of the line passing through (3, 2) that is perpendicular to 5x – 6y = 4. %3D 6z…

A: To find out the equation of line which passes through point (3, 2) and is perpendicular about the…

Q: write down the equation of the pair of straight lines joining the origin to the points of…

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Q: Find the equation of the line perpendicular to the line 4z – 3y = 12 and passing through the point…

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Q: Find the equation of the line of intersection of r +y+z = 0 and 2x – 3y + z = 0. Note: (0,0,0) is a…

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Q: Find the equation of the line perpendicular to -x - 4y = 6 and passes through the point whose…

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Q: Prove that the equation 2x2+3xy-2y2-x+3y-1=0 represent the pair of perpendicular lines

A: To Prove that the equation 2x2+3xy-2y2-x+3y-1=0 represent the pair of perpendicular lines

Q: Find equations of the lines that pass through the point (0, 4) and are (a) parallel toand (b)…

A: Given,         The equations of the lines that pass through the point 0,4 and the line 5x+2y=3.

Q: Find the equation of the line perpendicular to the lines x-1 x+1 쯤 and 1 and 2 == 2-1 2 2 4 3 = y-1…

A: (x-1)/2 = (y-1)/2 = (z-3)/2  And (x+1)/4 =y/3 =(z-1).

Q: Show that the lines d1: (7x-15)/ 2 = (7y+34)/ -5 = z/1 and d2: x/1 = (y+1)/-1 = (z+3)/-1 are…

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Q: Find an equation of the line that passes through the point (−4, 4) and is parallel to the line 9x −…

A: Rewrite the equation 9x–8y–6=0 as,

Q: Find the equation of the line that passes through the point (-1, 3) and is parallel to the line 5x –…

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Q: The line joining the origin and Pomt of of the linesr (X=1+2t,42-3+4t. y=-5+3t 2 Ction ,zet) and

A: Let the parameter of line L1 is t = t1 and the parameter of line L2 is t = t2. To find the point of…

Q: Find the equation of the line containing (-6, 6) which is parallel to the line 1 3. 1 y%3D 입-9 1 y =…

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Q: Find the equation of straigh line perpendicular to the line 5x – 2y = 7 and passing through point of…

A: the given line is  5x-2y=7 2y=5x-7 y=52x-72 here coefficient of x is 52 so the slope of the line is…

Q: Prove that the equation 2x2+3xy-2y2-x+3y-1=0 represents a pair of perpendicular lines

A: Solution: The objective is to find whether the given equation represents a pair of perpendicular…

Q: Consider the two lines  L1 : x=-2t, y=1+2t, z=3t L2 : x=-8+4s, y=1+4s, z=5+s Find the point of…

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Q: Find the point of intersection between the two lines: L:x 3t + 1, y = 2t - 1, z = t + 4 and L: 1 x-7…

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Q: 8. Find the equation of the line passing through the point (4, 5) and perpendicular to the line 3y =…

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Q: 2.) Find an equation of the line that is parallel to the line r(t) = and that passes through the…

A: To find an equation of the line that is parallel to the below line and passes through the point (1,…

Q: 45. Parallel to -3x + 4y = 12, passing through (-4, – 6)

A: The line is parallel to -3x+4y=12, passing through -4,-6

Q: Find equation of the line Passes through the Peint (-3,2,-1)-and parallel te the lineof intersection…

A: Given that: The given point is: (-3, 2, -1)The planes are: π1: x+2y+z=8 and π2:x+y-z=2

Q: Show that the equation of the line in R' through distinct points (1, Y1) and (x2, Y2) can be written…

A: We have to show that the equation of the line in R2 through distinct points x1,y1 and x2,y2 can be…

Q: parallel to the line 2x+3y+4=0

A: Equation of line passing through point and with slope m . (y-y1)=m(x-x1)  if two lines are parallel…

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.