write an equation in point slope form of the line through point j(4,1) with slope -4
Point-slope form of a linear equation:
y − y1 = m ( x − x1 )
( x1 , y1 ) is a point the line passes through
m = slope
In this case:
x1 = 4
y1 = 1
m = - 4
y − y1 = m ( x − x1 )
y − 1 = ( - 4 ) ∙ ( x − 4 )
y − 1 = ( - 4 ) ∙ x − 4 ∙ ( − 4 )
y − 1 = - 4 x + 16
Well, let's get this line the attention it deserves, shall we? Here we go:
So the point-slope form of a line is:
y - y₁ = m(x - x₁)
Where m is the slope and (x₁, y₁) is a point on the line. So for this line, with the slope of -4 and point J(4,1), we can replace m with -4 and x₁ with 4, and y₁ with 1:
y - 1 = -4(x - 4)
And there you have it! Your equation in point-slope form! But remember, laughter is the best medicine, so go spread some joy while you solve those equations!
To write the equation of a line in point-slope form, we need the point-slope formula:
(y - y₁) = m(x - x₁),
Where (x₁, y₁) represents a point on the line, and m is the slope of the line.
Given the point j(4,1) and a slope of -4, we can substitute the values into the formula:
(y - 1) = -4(x - 4).
Hence, the equation of the line in point-slope form is y - 1 = -4(x - 4).
To write an equation in point-slope form, we use the formula:
y - y₁ = m(x - x₁)
where:
- (x₁, y₁) represents the coordinates of the given point on the line (in this case, point J(4,1)),
- m represents the slope of the line.
For the equation with point J(4,1) and slope -4, we substitute the values into the point-slope form equation:
y - 1 = -4(x - 4)
Now, we simplify the equation:
y - 1 = -4x + 16
Finally, we can rearrange the equation to get it in the standard form:
4x + y = 17
So, the equation in point-slope form of the line through point J(4,1) with slope -4 is 4x + y = 17.