Find an equation of the line through (4, 6) and parallel to y= 2 x- 5.

Question

Must be in slope-intercept form!!

Answer 1

Hello, Caroline! The equation of a line that is parallel to another line has the same, exact slope, which in this case is 2. Next, plug in 4 for x and 6 for y in the equation y = 2x + b, in order to find your new y-intercept (b). Once you find your y-intercept, replace b with it in the equation y = 2x + b.

Answer 2

If the equation we need is parallel, then the slope (2x) will be the same. The only thing that will change is c, which is -5 in the original equation.

So let's change -5 to our variable, c, and plug our given point values into the given equation:

y = 2x + c becomes

6 = 2*4 + c = 8 + c

c = 6 - 8 = -2

Now put our new c value into the original equation:

y = 2x - 2