Which equation represents the line that has a slope of $\frac{1}{3}$13​​ and an x-intercept of $5$5​ ?ResponsesA.   $y-5=$y−5=​   $\frac{1}{3}$13​​ $x$x​A.  y minus 5 is equal to 1 thirdx - no response givenC.   $y-0=$y−0=​   $\frac{1}{3}$13​​ $\left(x+5\right)$(x+5)​C.  y minus 0 is equal to 1 thirdopen paren x plus 5 close paren - incorrectB.   $y-0=$y−0=​   $\frac{1}{3}$13​​ $\left(x-5\right)$(x−5)​B.  y minus 0 is equal to 1 thirdopen paren x minus 5 close paren - no response givenD.   $y-5=$y−5=​   $\frac{1}{3}$13​​ $\left(x-5\right)$

The equation of a line in slope-intercept form is given by y = mx + b, where m is the slope and b is the y-intercept. However, we are given the x-intercept instead of the y-intercept. The x-intercept is the value of x when y = 0. So, we can set up our equation as 0 = (1/3)x - b. We know that the x-intercept is 5, so we can substitute that into the equation to solve for b: 0 = (1/3)*5 - b. Solving for b, we get b = 5/3.

Therefore, the equation of the line is y = (1/3)x - 5/3. However, this is not in the form of any of the provided responses.

We can also express the equation of a line in point-slope form, which is y - y1 = m(x - x1), where (x1, y1) is a point on the line. We know that the line passes through the point (5, 0), so we can substitute these values into the equation to get y - 0 = (1/3)(x - 5). Simplifying, we get y = (1/3)(x - 5), which matches response B.

So, the correct response is B. y - 0 = (1/3)(x - 5).