Respuesta :
Answer:
see explanation
Step-by-step explanation:
The equation of a line in point- slope form is
y - b = m(x - a)
where m is the slope and (a, b) a point on the line
To calculate m use the slope formula
m = ( y₂ - y₁ ) / ( x₂ - x₁ )
with (x₁, y₁ ) = (6, 4) and (x₂, y₂ ) = (7, 2)
m = [tex]\frac{2-4}{7-6}[/tex] = [tex]\frac{-2}{1}[/tex] = - 2
There are 2 possible point- slope equations
Using (a, b) = (6, 4), then
y - 4 = - 2(x - 6)
OR
Using (a, b) = (7, 2), then
y - 2 = - 2(x - 7)
The point-slope equation of the line through (6,4) and (7,2) is y - 4 = -2(x - 6).
What is point-slope form of equation of straight line ?
The equation of a straight line in the form y - y1 = m(x - x1) where m is the slope of the line and (x1,y1) is the coordinate of the given point is known as the point-slope form . It is known as the point-slope form as it gives the definition of both the slope and coordinates of points.
How to find the given equation in point-slope form ?
Slope of the line, m is given by m = (y2 - y1)/(x2 - x1) .
∴ m = (2 - 4)/(7 - 6) = -2 .
Thus we take one point coordinate as (6,4), then the equation of straight line is -
⇒ y - 4 = -2(x - 6) .
Therefore, the point-slope equation of the line through (6,4) and (7,2) is y - 4 = -2(x - 6).
To learn more about point-slope form, refer -
https://brainly.com/question/18617367
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