Question

How do you write the equation given (0,0); (-2,7)?

Answer 1

See a solution process below:

Explanation:

First, we must determine the slope of the line running through the two points given in the problem. The slope can be found by using the formula: `m = (color(red)(y_2) - color(blue)(y_1))/(color(red)(x_2) - color(blue)(x_1))`

Where `m` is the slope and (`color(blue)(x_1, y_1)`) and (`color(red)(x_2, y_2)`) are the two points on the line.

Substituting the values from the points in the problem gives:

`m = (color(red)(7) - color(blue)(0))/(color(red)(-2) - color(blue)(0)) = -7/2`

Now, we can use the point-slope formula to write an equation for the line. The point-slope formula states: `(y - color(red)(y_1)) = color(blue)(m)(x - color(red)(x_1))`

Where `color(blue)(m)` is the slope and `(color(red)(x_1, y_1))` is a point the line passes through.

Substituting the slope we calculated and the values from the first point in the problem gives:

`(y - color(red)(0)) = color(blue)(-7/2)(x - color(red)(0))`

`y = color(blue)(-7/2)x`

We can also substitute the slope we calculated and the values from the second point in the problem giving:

`(y - color(red)(7)) = color(blue)(-7/2)(x - color(red)(-2))`

`(y - color(red)(7)) = color(blue)(-7/2)(x + color(red)(2))`

We can also take the first equation and write this in slope-intercept form. The slope-intercept form of a linear equation is: `y = color(red)(m)x + color(blue)(b)`

Where `color(red)(m)` is the slope and `color(blue)(b)` is the y-intercept value.

`y = color(red)(-7/2)x + color(blue)(0)`

Answer 2

`y=-7/2x`

Explanation:

The find the equation of a line or gradient, first find the slope via the formula: `m=(y_2-y_1)/(x_2-x_1)`

If we let `(0,0)->(color(red)(x_1),color(blue)(y_1))` and `(-2,7)->color(red)(x_2),color(blue)(y_2))` then,

`m=color(blue)(7-0)/color(red)(-2-0)=-7/2larr` This is the slope of the line/gradient

Now that we have found the slope we can find the equation via the point-slope formula:

`y-y_1=m(x-x_1)`;

by substituting `-7/2` for `m` and any of the two coordinates given. I will use `(0,0)` be make things easier. We let `(0,0)->(x_1,y_1)`

Thus,

`y-0=-7/2(x-0)`

If we simplify this, we simply get

`y=-7/2xlarr` This is our equation

Graph:

graph{-7/2x [-10, 10, -5, 5]}