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What is (-3/5,6);m=-1

User Nicu Surdu
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The equation of the line in standard form is 2x+3y=9.

To find the equation of a line given two points (−3,5) and (6,−1), you can use the point-slope form or slope-intercept form.

1. Using the slope-intercept form (y = mx + b):

Find the slope (m) using the formula:

m= y_2 −y_1/ x_2 −x_1

​​where

(x_1 ,y_1 ) = (−3,5) and (x_2​ ,y_2 ) = (6,−1).

m= −1−5/ 6−(−3) = −6/9 =− 2/3

Use one of the given points (−3,5) and the slope m to find the y-intercept (b) in the equation y=mx+b.

y=mx+b

5=− 2/3 ×(−3)+b

5=2+b

b=5−2=3

So, the equation of the line in slope-intercept form is

y=− 2/3 x+3.

2. Using the standard form (Ax + By = C):

We can convert the equation y=− 2/3 x+3 into the standard form.

x+3⟹ 2/3​ x+y=3

To eliminate fractions, multiply every term by 3:

2x+3y=9

Thus, the equation of the line in standard form is 2x+3y=9.

Question

What is the equation of the line in slope intercept form and standard form that passes through (-3,5) and (6,-1)?

User CrepeGoat
by
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