What is an equation of the line, in point-slope form, that passes through the given point and has the given slope?
point: (9, 3); slope: 4/9
y – 3 = 4 / 9 ( x – 9 )
add 3 to both sides
y – 3 + 3 = 4 / 9 ( x – 9 ) + 3
y = ( 4 / 9 ) ∙ x – ( 4 / 9 ) ∙ 9 + 3
y = ( 4 / 9 ) x – 4 + 3
y = ( 4 / 9 ) x – 1
Answer D is correct.
choices are : .
y – 9 =4/9 (x + 3)
B.
y – 9 = 4/9 (x – 3)
C.
y + 3 =4/9 (x – 9)
D.
y – 3 = 4/9 (x – 9)ices are :
Why did the line go to therapy? Because it had a slope problem!
Using the point-slope form of a line, we have:
y - y₁ = m(x - x₁)
where (x₁, y₁) is the given point and m is the slope.
Substituting the values, we get:
y - 3 = (4/9)(x - 9)
And there you have it! The equation of the line in point-slope form is y - 3 = (4/9)(x - 9).
To find the equation of a line in point-slope form, we need to know the coordinates of a point on the line (in this case, (9, 3)) and the slope of the line (in this case, 4/9).
The point-slope form of an equation is:
y - y1 = m(x - x1),
where (x1, y1) represents the coordinates of the point and m represents the slope.
Plugging in the values, we have:
y - 3 = (4/9)(x - 9).
This is the equation of the line in point-slope form that passes through the point (9, 3) and has a slope of 4/9.
y = m x + b
Where:
m is the slope
b is the y-intercept
In tis case:
y = ( 4 / 9 ) x + b
You know coordinates of one point ( 9 , 3 )
Replace x = 9 , y = 3 in equation:
y = ( 4 / 9 ) x + b
3 = ( 4 / 9 ) ∙ 9 + b
3 = 4 + b
Subtact 4 to both sides
3 - 4 = 4 + b - 4
- 1 = b
b = - 1
So:
y = ( 4 / 9 ) x - 1