# Passes through (-2, 5) and (3, 1). Write an equation in slope-intercept form for the line that satisfies each set of conditions.

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Another way of doing any kind of problems like these it's to use the "Point-Slope Form" and solve for "y". This will ALWAYS give you the answer in one shot:

Use the given points to find the Slope (or m):

`(x1,y1) = (3,1)`

`(x2, y2) = (-2,5)`

`m= (y2-y1) / (x2-x1) = (5-1) / (-2-3) = 4/-5`

Now use the Point-Slope Formula and solve for "y":

`y - y1 = m(x-x1)`

``y - 1 = -4/5 ( x - 3 )

y - 1 = -4/5 x + 12/5

y = -4/5 x + 17/5

Given the points are

`(x_1,y_1) =(-2,5)`

and

`(x_2,y_2) =(3,1)`

the slope of the line passing through the points is given as

`m = (y_2 - y_1)/(x_2 - x_1)`

`= (1-5)/(3-(-2))`

` = -4/5`

so the slope is `-4/5`

as the

slope m= -4/5

and the line passes through the point (x,y)= (3, 1)

the slope-intercept form of a line is

y= mx+b

from the above we know m = 3, so the line equation is

y= (-4/5)x+b--------------(1)

we need to find the value of b, as the line passes through the point

(x,y)= (3, 1 ), then on substituting we get

1 =(-4/5)*(3)+b

=> b = 1+ (12/5) = 17/5

so the equation of the line is

y = (-4/5)x+(17/5)