Question

Write an equation in slope-intercept form for the line that passes through (5,2) and is parallel to y=7/5x+4

Answer 1

We know that parallel lines have the same slope, this means that the searched line has the form

`y=(7)/(5)x+b`

This is because the slope is the coefficient of x on the given line equation:

`y=(7)/(5)x+4`

Now, we can find by y-intercept, denoted by b, by substituting the given point (5,2) into our line from above, that is,

`2=(7)/(5)(5)+b`

which gives

`2=7+b`

then, by subtracting 7 to both sides, we get

`-5=b`

or equivalently,

`b=-5`

Finally, by substituting this value into our line model, the answer is:

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