How to find an equation of the straight line passing through the points with coordinates (-1,5) and (4,-2), giving your answer in the form ax+by+c=0?

Holden Joyce

Holden Joyce

Answered question

2023-03-16

How to find an equation of the straight line passing through the points with coordinates (-1,5) and (4,-2), giving your answer in the form ax+by+c=0?

Answer & Explanation

duairceasrxtg

duairceasrxtg

Beginner2023-03-17Added 6 answers

The definition of the slope, m, of the line between two points, ( x 1 , y 1 ) and ( x 2 , y 2 ) is:
m = y 2 - y 2 x 2 - x 1
Using the given points to compute m:
m = - 2 - 5 4 - - 1 = - 7 5
The slope-intercept form of the equation of a line is:
y = m x + b
Using the slope and the point ( - 1 , 5 ) , allows us to substitute -1 for x, 5 for y, and - 7 5 for m, so that we may find the value of b:
5 = - 7 5 ( - 1 ) + b
5 = 7 5 + b
5 - 7 5 = b
25 5 - 7 5 = b
b = 18/5
The line passing between the two specified locations has the following slope-intercept form:
y = - 7 5 x + 18 5
But we want the form, a x + b y + c = 0 , multiply boths side by 5:
5 y = - 7 x + 18
Add 7 x - 18 to both sides:
7 x + 5 y - 18 = 0

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