equation of the line please help1

Question

 

equation of the line

1) write an equation of the line parallel  to x+2y=6 through (8,3) 2) find the equation of a line containing points (-2,8) and (3,5) 3) write an equation of the line parallel  to y=3x-2 through (1,-3) 4) write an equation of the line parallel  to x+y=-3 through (0,4) 5) write an equation of the line parallel  to 2x-y=1 through (-1,2) 6) write an equation of the line parallel  to x-y=-4 through (1,-3)

 

Answer 1

1.

Given equation  is x + 2y = 6 and point is (8,3)

Above equation write in slope - intercept form y = m1x + b.

y = (-1/2)x + 3

Compare the values both two equations

So, m1 = -1/2 and b = 3

So, a line parallel to it has slope of m1 = m2 = -1/2.

You know the slope and a point on the line, so use the point - slope form with (x1,y1) = (8,3) to write  equation of the line.

(y - y1) = m2(x - x1)

(y - 3) = -1/2(x - 8)

Apply distributive property: a(b - c) = ab - ac.

y - 3 = (-1/2)x + 4

Add 3 each side

y - 3 + 3 = (-1/2)x +  4 + 3

y  = (-1/2)x +  7

The equation is y  = (-1/2)x + 7.

Answer 2

3.

Given equation  is  y = 3x - 2 and point is (1, -3)

Above equation already write in slope - intercept form y = m1x + b.

Compare the values both two equations

So, m1 = 3 and b = -2

So, a line parallel to it has slope of m1 = m2 = 3.

You know the slope and a point on the line, so use the point - slope form with (x1,y1) = (1, - 3) to write  equation of the line.

(y - y1) = m2(x - x1)

(y - (-3)) = 3(x - 1)

Product of two same signs is positive.

(y + 3) = 3(x - 1)

Apply distributive property: a(b - c) = ab - ac.

y + 3 = 3x - 3

Subtract 3 from  each side

y + 3 - 3 = (-1/2)x -  3 - 3

y  = 3x - 6

The line equation is y  = 3x - 6.

Answer 3

4.

Given equation  is   x + y = - 3 and point is (0, 4)

Above equation  write in slope - intercept form y = m1x + b.

y = - x - 3

Compare the values both two equations

So, m1 = -1  and b = -3

So, a line parallel to it has slope of m1 = m2 = -1.

You know the slope and a point on the line, so use the point - slope form with (x1,y1) = (0, 4) to write  equation of the line.

(y - y1) = m2(x - x1)

(y - 4) = -1(x - 0)

y - 4 = - x

Add 4 to each side

y - 4 + 4 = - x + 4

y  = - x + 4

The line equation is y  = - x + 4.

Answer 4

5.

Given equation  is   2x - y = 1 and point is (-1, 2)

Above equation  write in slope - intercept form y = m1x + b.

y = 2x - 1

Compare the values both two equations

So, m1 = 2  and b = -1

So, a line parallel to it has slope of m1 = m2 = 2.

You know the slope and a point on the line, so use the point - slope form with (x1,y1) = (-1, 2) to write  equation of the line.

(y - y1) = m2(x - x1)

(y - 2) = 2(x - (-1))

Product of two same signs is positive.

(y - 2) = 2(x + 1)

Apply distributive property: a(b + c) = ab + ac.

y - 2 = 2x + 2

Add 2 to each side.

y - 2 + 2 = 2x + 2 + 2

y  = 2x + 4

The line equation is y  = 2x + 4.

 

Answer 5

6.

Given equation  is   x - y = - 4 and point is (1, - 3)

Above equation  write in slope - intercept form y = m1x + b.

y = x + 4

Compare the values both two equations

So, m1 = 1  and b = 4

So, a line parallel to it has slope of m1 = m2 = 1.

You know the slope and a point on the line, so use the point - slope form with (x1,y1) = (1, - 3) to write  equation of the line.

(y - y1) = m2(x - x1)

(y - (-3)) = 1(x - 1)

Product of two same signs is positive.

(y + 3) = 1(x - 1)

Apply distributive property: a(b + c) = ab + ac.

y + 3 = x - 1

Subtract 3 from  to each side.

y + 3 -3 = x - 1 - 3

y  = x - 4

The line equation is y = x - 4.

 

Answer 6

2.

Given points  are (-2, 8) and (3, 5).

The line passes through (x1,y1) = (-2,8) and (x2,y2) = (3,5). Find its slope.

m = y2 - y1/x2 - x1 = 5 - 8/3 -(-2)

Product of two same signs is positive.

m = -3/5

You know the slope and a point on the line, so use the point - slope form with either given point to  to write  equation of the line.

Choose (x1,y1) = (3,5)

(y - y1) = m(x - x1)

(y - 5) = -3/5(x - 3)

Apply distributive property: a(b - c) = ab - ac.

y - 5 = (-3/5)x + 9/3

Add 5 to each side.

y - 5 + 5 = (-3/5)x + 9/3 + 5

y  = (-3/5)x + 24/3

y  = (-3/5)x + 8

The line equation is y = (-3/5)x + 8.

 

Answer 7

1)write an equation of the line parallel  to x+2y=6 through (8,3)

Given equation is x+2y=6

The above equation passes through (8,3)

The parallel line equation is x+2y=k -----------(1)

then substitute x = 8 and y = 3

=>8 + 2(3) = k

=>8 + 6 = k

=>14 = k

=>k = 14

The value k = 14 substitute in equation (1)

=>x+2y=14

The required line equation is x+2y=14.

Answer 8

3)write an equation of the line parallel  to y=3x-2 through (1,-3)

Given equation is y=3x-2

The parallel line equation is y-3x=k -----------(1)

The above equation passes through (1,-3)

then substitute x = 1 and y = -3

=>-3 - 3(1) = k

=>-3 - 3 = k

=>-6 = k

=>k = -6

The value k = -6 substitute in equation (1)

=>y-3x=-6

The required line equation is y=3x-6.

Answer 9

Given equation  is x + 2y = 6 and point is (8,3)

Above equation write in slope - intercept form y = m1x + b.

x+2y=6

add each side -x

-x +x +2y= -x+6

2y = -x+6

devide each side by 2

2y/2= -x/2+6/2

y = (-1/2)x + 3

Compare the values both two equations

So, m1 = -1/2 and b = 3

So, a line parallel to it has slope of m1 = m2 = -1/2.

You know the slope and a point on the line, so use the point - slope form with (x1,y1) = (8,3) to write  equation of the line.

(y - y1) = m2(x - x1)

(y - 3) = -1/2(x - 8)

Apply distributive property: a(b - c) = ab - ac.

y - 3 = (-1/2)x + 4

Add 3 each side

y - 3 + 3 = (-1/2)x +  4 + 3

y  = (-1/2)x +  7

2y = -1x +14

x+2y-14 = 0

The line equation is x+2y-14 = 0

Answer 10

Given equation  is  y = 3x - 2 and point is (1, -3)

Above equation already write in slope - intercept form y = m1x + b.

Compare the values both two equations

So, m1 = 3 and b = -2

So, a line parallel to it has slope of m1 = m2 = 3.

You know the slope and a point on the line, so use the point - slope form with (x1,y1) = (1, - 3) to write  equation of the line.

(y - y1) = m2(x - x1)

(y - (-3)) = 3(x - 1)

Product of two same signs is positive.

(y + 3) = 3(x - 1)

Apply distributive property: a(b - c) = ab - ac.

y + 3 = 3x - 3

Subtract 3 from  each side

y + 3 - 3 = 3x -  3 - 3

y  = 3x - 6

The line equation is y  = 3x - 6.