option B
ANSWER:
The equation that is parallel to the line y = −5x + 2 and passes through the point (0, 3) is y = -5x + 3
SOLUTION:
We need to find Write an equation that is parallel to the line y = −5x + 2 and passes through the point (0, 3).
Given, Equation is y = -5x + 3 ----- eqn (1)
Given point P(0,3)
The above equation is in slope intercept form y = mx + c, Where m is slope and c is intercept made on x-axis.
Comparing equation 1 with y = mx + c we get m =-5 and c =3
Two parallel equations will always has the same slope.
So the required equation slope is also -5 that is m=-5 and it passes through the point p
Now, by using point slope form [tex]y-y_{1}=m\left(x-x_{1}\right)[/tex] ---- eqn(2),
where m is slope and [tex]\left(x_{1}, y_{1}\right)[/tex] point on that line.
Put [tex]x_{1}=0, y_{1}=3[/tex] and m =-5 in eqn (2)
y – 3 = -5(x – 0)
y – 3 = -5x
y = -5x +3
Hence the equation that is parallel to the line y = −5x + 2 and passes through the point (0, 3) is y = -5x + 3, i.e. option B
