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

Textbook Question

Chapter 2, 2.4 - Problem 9 - Glencoe Algebra 2 (1st Edition, McGraw-Hill Education).
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kspcr111 | In Training Educator

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Given the points are

`(x_1,y_1) =(-3,5)`

and

`(x_2,y_2) =(2,2)`

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

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

    `= (2-5)/(2-(-3))`

   ` = -3/5`

so the slope is `-3/5`

as the

 slope `m= -3/5`

and the line passes through the point `(x,y)= (2, 2)`

the slope-intercept form of a line is

`y= mx+b`

from the above we know `m = -3/5` , so the line equation is 

`y= (-3/5)x+b` --------------(1)

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

`(x,y)= (2, 2 )` , then on substituting we get

`2 =(-3/5)*(2)+b`

=> `b = 2+ (6/5) = 16/5`

so the equation of the line is

`y= (-3/5)x+(16/5)`

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