the problem reads:
Write the equation of the line which passes through the point (2,1) and is parallel to another line with equation y = (5)/(2) x + 6
the answer i get is the following is this correct though
y = (5)/(2) x - 4
Since your new line is parallel to
y=(5/2)x + 6 it has the same slope
So it must be y = (5/2)x + b
Substitute x=2 and y=1 into that to find b
so your answer is right
i get my same equation as i stated previously is that what you get
b i get -4
Yes, you are correct. The equation of the line that passes through the point (2,1) and is parallel to y = (5/2)x + 6 is y = (5/2)x - 4.
To find this equation, you recognized that parallel lines have the same slope. Since the given line has a slope of 5/2, the new line must also have a slope of 5/2.
Using the slope-intercept form, y = mx + b, you substituted the point (2,1) into the equation and solved for the value of b.
Plugging in x = 2 and y = 1, you have the equation 1 = (5/2)(2) + b. Solving for b, you find that b = -4.
Therefore, the equation of the line is y = (5/2)x - 4, which matches your answer. Well done!