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:
[tex]x_{1} =-4[/tex] and [tex]y_{1} =7[/tex]
[tex]y-y_{1} =m(x-x_{1} )[/tex] 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
Step-by-step 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:
[tex]x_{1} =-4[/tex] and [tex]y_{1} =7[/tex]
[tex]y-y_{1} =m(x-x_{1} )[/tex] 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).
