Write an equation in point slope form that passes through (5,1), (-3,4) then write an equation in standard form and in slope intercept form.

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sciencesolve's profile pic

sciencesolve | Teacher | (Level 3) Educator Emeritus

Posted on

You need to remember the what the point slope form of equation of the line is such that:

`y - y_1 = m(x - x_1)`

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

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

`y - 1 = 3/(-8)*(x-5)`

`y - 1 = -3/8(x - 5)`

You need to remember what is the slope intercept form of equation such that:

`y = mx + b`

Hence, you need to isolate y to the left side and to open the brackets such that:

`y = -3x/8 + 15/8 + 1`

`y = -3x/8 + (15+8)/8`

`y = -3x/8 + 23/8`

You need to write the standard form of equation of line, hence, you need to bring the terms in equation `y = -3x/8 + 23/8`  to a common denominator such that:

`8y = -3x + 23`

You need to move all terms to the left side such that:

`3x + 8y - 23 = 0`

Hence, evaluating the point slope form yields `y - 1 = -3/8(x - 5),`  evaluating the slope intercept form yields `y = -3x/8 + 23/8`  and evaluating the standard form yields `3x + 8y - 23 = 0.`

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Wiggin42's profile pic

Wiggin42 | Student, Undergraduate | (Level 2) Valedictorian

Posted on

(5,1), (-3,4)

Given two points we can solve for slope: 

4 - 1 / (-3 - 5) = -3/8

Point slope formula: y - y1 = m(x - x1) Pick any point!)

y - 4 = (-3/8)(x +3) 

To get into slope-intercept, solve for y: 

y - 4 = (-3/8)x - (9/8)

y = (-3/8)x + 23/8

To get into standard form, get rid of the fractions and keep all therms on the same side: 

Multiply out by 8:

8y = -3x + 23

Get all terms on the same side:

3x + 8y -23 = 0

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