write an equation in slope intercept form for the line that passes through (3,7) and (7,4)

Question

slope intercept form for the line that passes through points

Answer 1

Given points say (x1,y1) = (3,7)

(x2,y2) = (7,4)

Slope of two points is m =(y2-y1)/(x2-x1)

m = 4-7/7-3

= -3/4

Line equation is y-y1 = m(x-x1)

y-7 = -3/2(x-3)

Cross multiplication.

2(y-7) = -3(x-3)

2y-14 = -3x+9

Add 14 to each side.

2y-14+14 = -3x+9+14

2y = -3x+23

Divide to each side by 2.

2y/2  = -3x/2+23/2

y = (-3/2)x+23/2

Slope intercept of the given line through the points is y = (-3/2)x+23/2.

Comments

please check your answer, y - 7 = - 3/4 (x - 3)
y - 7 = - 3/4 (x - 3)
Cross multiplication.
4(y - 7) = - 3(x - 3)
4y - 28 = - 3x + 9
Add 28 to each side.
4y = - 3x + 9 + 28
4y = - 3x + 37
Divide to each side by 4.
y = - 3/4 x + 37/4

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You are correct :)

Answer 2

The line equation is y = mx + b

m = (y2 - y1) / (x2 - x1)

= ( 4 - 7 ) / (7- 3)

= -3 / 4

 

Line equatio is y = 3/4x + b

Find y-intercept by substituing any point on the line say (3, 7))

7 = - 3/4 * 3 + b

b = 7 + 9 /4 = 37/ 4

The line equation is y = -3/4 x + 37/4