Write an equation in slope intercept form for a line that is parallel to 6x-y=1 and passes through the point (-2,2)

Answer 1

First change the given equation into slope-intercept form.

Slope-intercept form is y = mx + b (where m is the slope an b is the y intercept)

6x - y = 1

subtracting 6x from both sides we are left with

-y = -6x + 1

But, we don't want a negative y, so let's multiply everything by a -1.

Now, y=6x -1.

The slope is 6 and the y intercept is -1.

The second line is parallel to this line, and so we know that the slope is the same.

It passes through the point (-2, 2).

Now our formula for our new equation is

y - y₁= m(x - x₁)

Substituting what we know about our new equation, we now have

y - 2 = (6) [x - (-2)]

Doing the math,

y - 2 = 6x + 12

y = 6x + 14

Hope this helps.

Answer 2

The first thing you must know for this problem is what parallel lines on a coordinate system means mathematically, that is, that the lines have the same slope.

Begin with the general slope-intercept form:

y = mx + b

Now plug in what you know. Determine the slope of the original line by converting it to slope-intercept

(y = 6x -1) or by using the mini formula for standard form ( -a/b). The slope, in either technique is 6.

So we start with y = 6x +b

Now we have a scary equation with three variables. If we only knew two of them, we'd be in great shape. And we DO. We have the point (-2,2) which is an x and a y value. So we'll plug them in to solve for b:

2 = 6(-2) + b

2= -12 + b (simplifying)

14 = b (add 12 to both sides)

Now we know our equation: y = 6x + 14

Use your graphing app to confirm that the line does go through (-2,2)

Best wishes!