Question

Which equation represents a line that passes through (4, 1/3) and has a slope of 3/4

Answer 1

Answer:  9x - 12 y =32

Step-by-step explanation:

Since, the equation of a line passes through one point $(x_1,y_1)$ and having the slope m is,

$y-y_1 = m(x-x_1)$

Here, $x_1 = 4$, $y_1 = 1/3$ and m= 3/4

Therefore, equation of the line,

$y-1/3 = 3/4(x-4)$

⇒ 3y -1 = 9/4 (x-4)

⇒ 12 y - 4 = 9x - 36

⇒ 9x - 12y = - 4 + 36

⇒ 9x +12y = 32

Which is required equation of the line.

Answer 2

Y = mx + b
m = slope of the line
b= y-intercept

Since you are given the point (4,1/3), the y-value is 1/3.
So plug in the numbers and solve for b:
(1/3)= (3/4)*(4) + b

After you solve the equation for b, you should get -2 2/3 or -8/3

No rewrite the equation with the y-intercept, b.

y = (3/4 x) - (8/3)