Question

Find the equation of a line that is parallel to y = 2x + 7, and passes through the point (-4, 7)

Find the equation of a line that is perpendicular to y = 2x + 7, and passes through the point (-4, 7)

Answer 1

Parallel lines have the same slope. Perpendicular lines have negative reciprocal slopes.

Answer 2

Answer to Q1:

y=2x+15

Step-by-step explanation :

We have to find an equation that is parallel to y=2x+7 and passes through the point (-4,7).

y=mx+c is equation of line where m is slope and c is y-intercept.

The slope of Parallel lines are equal.

m=2 and a point (-4,7) is given:

`x_(1) =-4` and
`y_(1) =7`

`y-y_(1) =m(x-x_(1) )` is a point slope form of equation.

Hence,putting the value of m and given point in above equation,we get

y-(7)=2(x-(-4))

y-7=2(x+4)

y-7=2x+8

Adding 7 to both sides of above equation,we get

y-7+7=2x+8+7

Add like terms,

y+0=2x+15

y=2x +15 is equation of line that is parallel to y=2x+7 and passes through the point (-4,7).

Answer to Q2:

y=-1/2x+5

Explanation:

We have to find an equation that is perpendicular to y=2x+7 and passes through the point (-4,7).

y=mx+c is equation of line where m is slope and c is y-intercept.

The slope of Perpendicular lines are negative reciprocals of each other.

hence, slope of line perpendicular to y=2x+7 is -1/2.

m=-1/2 and a point (-4,7) is given:

`x_(1) =-4` and
`y_(1) =7`

`y-y_(1) =m(x-x_(1) )` is a point slope form of equation.

Hence,putting the value of m and given point in above equation,we get

y-7=-1/2(x-(-4))

y-7=-1/2(x+4)

y-7=-1/2x-1/2(4)

y-7=-1/2x-2

adding 7 to both sides of above equations,we get

y-7+7=-1/2x-2+7

add like terms

y+0=-1/2x+5

y=-1/2x+5 is equation of line that is perpendicular to y=2x+7 an passes through the point (-4,7).