Question

How do you write the equation in slope intercept form given (-5,0) and (3,3)?

Answer 1

See the entire solution process below:

Explanation:

First, we need to determine the slope for this equation. 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)(3) - color(blue)(0))/(color(red)(3) - color(blue)(-5)) = (color(red)(3) - color(blue)(0))/(color(red)(3) + color(blue)(5)) = 3/8`

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.

We can substitute the slope we calculated and one of the points from the problem for `x` and `y` and solve for `b`:

`3 = (color(red)(3/8) xx 3) + color(blue)(b)`

`3 = color(red)(9/8) + color(blue)(b)`

`3 - 9/8 = -9/8 + color(red)(9/8) + color(blue)(b)`

`(3 xx 8/8) - 9/8 = 0 + color(blue)(b)`

`24/8 - 9/8 = color(blue)(b)`

`15/8 = color(blue)(b)`

Substituting this result and the slope we calculated into the formula gives:

`y = color(red)(3/8)x + color(blue)(15/8)`

Answer 2

The equation of the line in slope-intercept form is `y= 3/8 x+1 7/8`

Explanation:

The slope of the line passing through `(-5,0) and (3,3)` is `m= (y_2-y_1)/(x_2-x_1)= (3-0)/(3+5)=3/8`

Let the equation of the line in slope-intercept form be `y=mx+c or y=3/8x+c` The point (-5,0) will satisfy the equation . So, `0= 3/8*(-5)+c or c= 15/8 = 1 7/8`

Hence the equation of the line in slope-intercept form is `y= 3/8 x+1 7/8` graph{3/8x+15/8 [-10, 10, -5, 5]} [Ans]