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

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)#

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]