How to find the equation in slope - intercept form, of the line passing through the points (-1, 2) and (3, -4)?

Armani Vang

Armani Vang

Answered question

2023-02-06

How to find the equation in slope - intercept form, of the line passing through the points (-1, 2) and (3, -4)?

Answer & Explanation

summatimeqtvmg

summatimeqtvmg

Beginner2023-02-07Added 5 answers

First, we need to determine the slope of the line for the equation. The slope can be found by using the formula: m = y 2 - y 1 x 2 - x 1
Where m is the slope and ( x 1 , y 1 ) and ( x 2 , y 2 ) are the two points on the line.
The result of substituting the values from the problem's points is:
m = - 4 - 2 3 - - 1 = - 4 - 2 3 + 1 = - 6 4 = - 3 2
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.
Because we have calculated the slope and the problem gives us a point from the line, we can substitute the slope we calculated for m and we can substitute the values from either of the points in the problem and solve for b :
2 = ( - 3 2 × - 1 ) + b
2 = 3 2 + b
- 3 2 + 2 = - 3 2 + 3 2 + b
- 3 2 + ( 2 2 × 2 ) = 0 + b
- 3 2 + 4 2 = b
1 2 = b
The equation can now be expressed in slope-intercept form by substituting the calculated slope and #b# value into the formula:
y = - 3 2 x + 1 2

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