Question

How do you write an equation of a line going through (0,7), (3,5)?

Answer 1

See the entire solution process below:

Explanation:

First, we need to determine the slope of the line going through the two points. 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)(5) - color(blue)(7))/(color(red)(3) - color(blue)(0)) = -2/3`

Now, we can use the point-slope formula to find an equation going through the two points. 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 gives:

`(y - color(red)(7)) = color(blue)(-2/3)(x - color(red)(0))`

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

`(y - color(red)(5)) = color(blue)(-2/3)(x - color(red)(3))`

We can also solve the first equation for `y` to transform the equation to 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) = color(blue)(-2/3)x`

`y - color(red)(7) + 7 = -2/3x + 7`

`y - 0 = -2/3x + 7`

`y = color(red)(-2/3)x + color(blue)(7)`

Answer 2

See below.

Explanation:

Since a point is given at `(0, 7)`, you know already that the y - intercept has to be 7. Therefore, you know b in the following equation:

`y = mx + b`

Now, use the slope formula to find m, the slope.

`(7-5)/(0-3) = (2)/(-3)`

So the equation must be: `y =- 2/3x + 7`

Hope that helps!!