I need help on a problem don't know the answer or how to get it

Question

What is the equation of the line that passes through the point (7,0) and is parallel to the line represented by the equation y=2.5x+3.5?

Answer 1

a line with slope 2.5 through (7,0)

parallel lines have the same slope = the coefficient of the x term when the equation is solved for y

slope = the difference in y coordinates divided by difference in x coordinates

(y-0)/(x-7) =2.5

y = 2.5(x-7)

y = 2.5x - 17.5

Answer 2

y = mx + b

m is the slope, b is the y-intercept (the value of y when x is 0).

In this case, we need to find a line that crosses the point (7,0), which is actually an x intercept (the value of x when y is 0). More than that though, we know that this line must be parallel to the given line. For lines to be parallel (never cross), their slopes must be exactly equal. Therefore, the line we're trying to find must have a slope of 2.5 (given by the 2.5 in the original line).

With all of this information, we can deduce that the equation we're trying to solve is 0 = (2.5*7) + C

this can be read as (When y is 0, the slope is 2.5, and x is 7, what is the value of C necessary to make the equation true). Once we have this, we'll know the equation for our line. Solving the above (2.5 * 7) = 17.5, and then we need C to be equal to -17.5 to get the total value to 0. Therefore, the equation of a parallel line that crosses the point (7,0) would be y = 2.5x - 17.5