please help me with this problem i am having tons of trouble

Question

Write an equation of the line   

​[minus−​5,5] by [5,−​5]

Express the answer using either the general form or the​ slope-intercept form of the equation of a line.

Answer 1

Points are indicated by parentheses: (-5, 5) and (5, -5).

The slope, m, is (-5 - 5) / (5 + 5), or -1

y = -x + b

5 = -(-5) + b

5 = 5 + b

0 = b

y = -x

Answer 2

Let's use the form y = mx + b

m is the slope and b is the y intercept (where x = 0)

You are given two points:

x = -5, y = 5

x = 5, y = -5

The slope (m) is defined as the difference in y values,divided by the difference in x values, so:

m = (5 - (-5)) / (-5 - 5) = 10 / -10

m = -1

Next, from the symmetry of the given points, we can see that the line includes the point (0, 0), therefore the y intercept is 0.

So:

y = -x

The more general way to do this is to create 2 equations in m and b, using the given x and y values.

Plugging in (5, -5), we get:

-5 = m*5 + b

And--using (-5, 5), we get

5 = m*(-5) + b

Solving this pair of equations, will give you m = -1 and b = 0

Answer 3

(-5,5) and (5,-5) are points that the line goes through I assume

the slope is (y2-y1)/(x2-x1)

(5-[-5])/(-5-5)=10/-10=-1

y=mx+b is the equation of a line where m=slope and b=y-intercept

y=-1(x)+b or,...

y=-x+b

pick either point and substitute

5=-(-5)+b

5=5+b

b=0

y=-x is the equation of the line

Answer 4

Maybe you mean the line connecting those two points, (-5,5) and (5,-5). It goes through the origin, so its y intercept is zero. The two points are mirror reflections of each other, if the mirror is the line y=x It goes down 1 for every change of 1 to the right. So it's slope is negative 1.

the equations is y=-x y=(slope)x + y intercept

You can see that from looking at either point -5 the x value is minus the y-value of 5 x=-y

Same with the other point (5,-5) the x value is -(-5).

Or you can use the two point formula setting slopes equal. Slope is rise over run, the amount y rises over how much x increases or runs horizontally. (y--5)/(x-5) = (y-5)/(x--5) or (y+5)/(x-5) = (y-5)/(x+5)

Multiply by least common denominator, (x-5)(x+5) or cross multiply to get (y+5)(x+5) = (y-5)(x-5)

Expand and simplify: xy+25+5x+5y = xy+25-5x-5y the xy terms cancel, the 25 terms cancel

leaving 5x+5y= -5x-5y. Divide by 5 to get x+y=-x-y or 2y=-2x or y=-x

By general form, you might mean ax+by+c=0

Then you could convert y=-x into x+y = 0 The two points, each of them, have x and y values that added together equal zero. 5 + (-5) = 0 and -5 + 5 = 0