Write an equation in point-slope form for the line through the given point with the given slope. (-3,-5); m=-2/5
Straight line Equation in point slope form:
y – y1 = m ( x – x1 )
In this case:
x1 = - 3 , y1 = - 5 , m = - 2 / 5
y – y1 = m ( x – x1 )
y – ( - 5 ) = ( - 2 / 5 ) [ x – ( - 3 ) ]
y + 5 = ( - 2 / 5 ) ( x + 3 )
Subtract 5 to both sides
y + 5 - 5 = ( - 2 / 5 ) ( x + 3 ) - 5
y = ( - 2 / 5 ) ( x + 3 ) - 5
y = ( - 2 / 5 ) ∙ x + ( - 2 / 5 ) ∙ 3 - 5
y = ( - 2 / 5 ) ∙ x - 6 / 5 - 5
y = ( - 2 / 5 ) ∙ x - 6 / 5 - 25 / 5
y = ( - 2 / 5 ) x - 31 / 5
To write an equation in point-slope form for a line, you need the coordinates of a point on the line and the slope of the line. We are given the point (-3, -5) and the slope m = -2/5.
The point-slope form of a linear equation is y - y1 = m(x - x1), where (x1, y1) represents the coordinates of the point and m represents the slope.
Substituting the given values into the equation, we have:
y - (-5) = (-2/5)(x - (-3))
Simplifying further:
y + 5 = (-2/5)(x + 3)
This is the equation in point-slope form for the line through the point (-3, -5) with a slope of -2/5.