Help my stem exams are coming up

Question

Find the equation for a line containing the given point and having the given slope.

(3, -1), m=-1

Answer 1

Hi!

When you're given a point on the line and the slope, there's a series of simple steps to do to find the answer.

Starting with our general equation:

y=mx+b

where m is the slope and b is the y-intercept.

Plugging in our point and slope:

(-1) = (-1)(3) + b

We can now solve for b to find our y-intercept of the line.

Multiply 3 & -1

-1 = -3 + b

Subtract b from both sides

2 = b

Now plug the slope and y-intercept into the general formula and we have the final equation of the line.

y=-1x + 2

Answer 2

The answer to this question depends on which format of the linear equation you are asked to write it in. If you are asked to write it in slope-intercept form (y = mx + b), then:

M = slope; b = y-intercept

Slope or m = -1 (that info was given)

To find b (y-intercept):

y = -1x + b

Plug in the x and y values from the point given above (3, -1)

-1 = (-1)(3) + b

-1 = -3 + b

+3. +3

2 = b or b = 2

So..... y = -x + 2

If you're asked to write in point-slope form, just plug in everything that was given in the question:

(y - y₁) = m(x - x₁)

(y - (-1)) = -1(x - 3)

(y + 1) = -1(x - 3)