y=2/5x+9 write an equation that is parallel to the given line and passes through the point (0, 2)

A lines are paralell when the slopes are equal all we need to do is tell the graph togo through (0,2)
y=mx+b ;

m= slope,

x and y are the cordinates given, (0,2) respectively,

b is what we can change to make the line go through the right point.

plug in the coordinates to find the matching b value.

2=2/5(0)+b
2=0+b
b=2
eq. for parallel line
y=2/5(x)+2

same idea for a perpedicular line except for to be perpedicular the second line's slope must be a recipricol and oppositely signed.

To get the slope you flip the original and multiply it by -1.
Then whats left is to find b again using your new slope.

using form y=mx+b , m is slope, b is y-axis intercept (a point on the gaph where x=0)

A) Two lines are parallel, they have same slope

y=2/5x+9 has slope 2/5, the new line has slope 2/5 too

the new line pass through point (0,2), b=2

solve A: y=2/5x+2

B) Two lines are perpendicular, if line1 slope m₁, line2 slope m₂   m₁=-1/m₂

y=2/5x+9 has slope 2/5, so the new line has slope -1/(2/5)=-5/2

new line pass through point (0,3), the y-axis intercept is 3

solve B: y=(-5/2)x+3