A line passes through the points (5, 3)

Question

and has a slope of m=4/9
. What is the point-slope form of the equation for this line?(1 point)
Responses

y+1=4/9(x+4)
y plus 1 is equal to 4 ninths times open paren x plus 4 close paren - incorrect

y−3=4/9(x−5)
y minus 3 is equal to 4 ninths times open paren x minus 5 close paren - no response given

y+3=4/9(x+5)
y plus 3 is equal to 4 ninths times open paren x plus 5 close paren - no response given

y−3=5/3(x−5)

Answer 1

To find the point-slope form of the equation of a line that passes through a given point (5, 3) with a slope of \( m = \frac{4}{9} \), we can use the point-slope form of a line, which is given by:

\[ y - y_1 = m(x - x_1) \]

Here, \( (x_1, y_1) \) is a point on the line. In this case, we have \( x_1 = 5 \) and \( y_1 = 3 \). Now we can substitute these values into the point-slope form:

\[ y - 3 = \frac{4}{9}(x - 5) \]

This matches the response:

y − 3 = 4/9(x − 5)

So, the correct point-slope form of the equation for the line is:

y − 3 = 4/9(x − 5)

This is the correct answer.