How do you write an equation in slope intercept form using the points (4,-3) , (2,3)?

Question

Kennedy Adams · Accepted Answer

#y = -3x + 9#

First, we will write and equation in point-slope form and then convert to slope-intercept form.

To use the point-slope form we must first determine the slope.

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)(-3))/(color(red)(2) - color(blue)(4))#

#m = (color(red)(3) + color(blue)(3))/(color(red)(2) - color(blue)(4))#

#m = 6/-2 = -3#

We can now use this calculated slope and either point to write the equation in point-slope form.

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.

Again, substituting gives:

#(y - color(red)(-3)) = color(blue)(-3)(x - color(red)(4))#

#(y + color(red)(3)) = color(blue)(-3)(x - color(red)(4))#

We can now convert this 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.

We can solve our equation for #y#:

#(y + color(red)(3)) = color(blue)(-3)(x - color(red)(4))#

#y + color(red)(3) = (color(blue)(-3) xx x) - (color(blue)(-3) xx color(red)(4))#

#y + 3 = -3x - (-12)#

#y + 3 = -3x + 12#

#y + 3 - color(red)(3) = -3x + 12 - color(red)(3)#

#y + 0 = -3x + 9#

#y = -3x + 9#

Savannah Anderson · Answer

undefined To write an equation in slope-intercept form (y = mx + b) using the given points (4, -3) and (2, 3), follow these steps:

1. Find the slope (m) using the formula: 
   m = (y2 - y1) / (x2 - x1)
2. Substitute the coordinates of one of the points into the slope formula to find the slope.
3. Once you have the slope (m), substitute it along with the coordinates of one of the points into the slope-intercept form equation (y = mx + b) and solve for the y-intercept (b).
4. Write the equation using the slope (m) and y-intercept (b).

Let's go through the steps:

1. Find the slope:
   m = (3 - (-3)) / (2 - 4)
     = (3 + 3) / (2 - 4)
     = 6 / -2
     = -3

2. Choose one of the points to substitute into the slope-intercept form equation. Let's use the point (4, -3):
   -3 = (-3)(4) + b
   -3 = -12 + b
   b = -3 + 12
   b = 9

3. Write the equation using the slope (m) and y-intercept (b):
   y = -3x + 9