through: (5, 2), parallel to y = 7 5 x + 4

Question

please explain in detail

Answer 1

Note that two lines are considered to be parallel if they have the same slope.

In this case, we are looking for a line parallel to y = (7/5)x + 4

Recall that a line in this form is in a form called slope-intercept form (y = mx + b), where "m" is the slope and "b" is the y-intercept of the line.

Therefore the slope of the line is m = (7/5)

Now, to find a line that passes through the point (5,2) we can use another formula for a line called point-slope form: y - y₁ = m(x - x₁) where (x₁,y₁) = (5,2) is the point that the line intercepts.

So, if we plug in the information that we have, m = (7/5) and (x₁,y₁) = (5,2) we get,

y - y₁ = m(x - x₁)

y - 2 = (7/5)(x - 5)

All that is left to do is simplify and put this equation back into slope-intercept form (y = mx + b)

y - 2 = (7/5)(x - 5)

y - 2 = (7/5)x - (7/5)(5) [distribute]

y - 2 = (7/5)x - 7 [ (7/5)(5) = 7 ]

y = (7/5)x - 5 [add 2 to both sides]

Therefore, the equation of a line that is parallel to y = (7/5)x + 4 and passes through the point (5,2) is

y = (7/5)x - 5