Write an equation of the line through $(-4,-5)$ having slope $\frac{20}{7}$. Give the answer in standard form.

Step 1 ：Given a point on the line (-4,-5) and the slope of the line is \(\frac{20}{7}\).

Step 2 ：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.

Step 3 ：Substitute the given values into the equation to solve for \(b\): \(-5 = \frac{20}{7}*(-4) + b\).

Step 4 ：Solving the above equation gives \(b = 6.428571428571429\).

Step 5 ：Now that we have the y-intercept, we can write the equation of the line in slope-intercept form: \(y = \frac{20}{7}x + 6.428571428571429\).

Step 6 ：However, the question asks for the equation in standard form, which is \(Ax + By = C\).

Step 7 ：We can convert the slope-intercept form to standard form by multiplying each side of the equation by 7 to eliminate the fraction, and then rearranging the terms: \(7y = 20x + 45\).

Step 8 ：Rearranging the terms gives the equation in standard form: \(-20x + 7y = 45\).

Step 9 ：Final Answer: The equation of the line in standard form is \(\boxed{-20x + 7y = 45}\).