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)?