How to write the equation of a line in point slope form and slope intercept form given point (6, -3) and has a slope of 1/2?

fagiolinow8xk

fagiolinow8xk

Answered question

2023-02-17

How to write the equation of a line in point slope form and slope intercept form given point (6, -3) and has a slope of 1/2?

Answer & Explanation

Malia Klein

Malia Klein

Beginner2023-02-18Added 5 answers

The equation of a line in point-slope form is
y - y 1 = m ( x - x 1 )
Where #m# is the slope and the point is ( x 1 , y 1 )
For this problem
m = 1 2
x 1 = 6
y 1 = - 3
Plug in the values
y - ( - 3 ) = 1 2 ( x - 6 )
Simplify the signs
y + 3 = 1 2 ( x - 6 )
This is the point-slope form of the equation
Now solve for y to get the slope-intercept form.
y + 3 = 1 2 ( x - 6 )
By using the distributive property, the parentheses will be removed.
y + 3 = 1 2 x - 3
Now isolate the y using the additive inverse
y + 3 - 3 = 1 2 x - 3 - 3
y = 1 2 x - 6
This is how the equation looks in slope-intercept form.
marinacabello82g3

marinacabello82g3

Beginner2023-02-19Added 1 answers

The point-slope form of a linear equation is:
( y - y 1 ) = m ( x - x 1 )
Where ( x 1 , y 1 ) is a point on the line and m is the slope
The result of substituting the slope and values from the problem's point is:
( y - - 3 ) = 1 2 ( x - 6 )
( y + 3 ) = 1 2 ( x - 6 )
The slope-intercept form of a linear equation is: y = m x + b
Where m is the slope and b is the y-intercept value.
The point-slope equation for y can be solved, resulting in:
( y + 3 ) = 1 2 ( x - 6 )
y + 3 = ( 1 2 × x ) - ( 1 2 × 6 )
y + 3 = 1 2 x - 6 2
y + 3 = 1 2 x - 3
y + 3 - 3 = 1 2 x - 3 - 3
y + 0 = 1 2 x - 6
y = 1 2 x - 6

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