Write an equation of the line through (−5,−4) having slope $$ \frac{17}{16} $$ Give the answer in standard form.

To write the equation of a line through the point $(-5, -4)$ with slope $ \frac{17}{16} $, we can start with the point-slope form of the equation:

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

where:
- $ m = \frac{17}{16} $ (the slope),
- $ (x_1, y_1) = (-5, -4) $ (the point on the line).

Substitute the values:

\[
y - (-4) = \frac{17}{16}(x - (-5))
\]

Simplify the equation:

\[
y + 4 = \frac{17}{16}(x + 5)
\]

Next, we distribute $ \frac{17}{16} $ on the right-hand side:

\[
y + 4 = \frac{17}{16}x + \frac{85}{16}
\]

To eliminate the fraction, multiply both sides of the equation by 16:

\[
16(y + 4) = 17x + 85
\]

Simplify both sides:

\[
16y + 64 = 17x + 85
\]

Now, rearrange the terms to get the equation in standard form $Ax + By = C$:

\[
17x - 16y = -21
\]

Thus, the equation of the line in standard form is:

\[
17x - 16y = -21
\]

Would you like a breakdown of any steps or further explanation? Here are some follow-up questions:

1. How do you convert from point-slope form to standard form?
2. What is the significance of the standard form in linear equations?
3. How do you find the slope of a line between two points?
4. Can you find the equation of a line with a slope of 0?
5. How do you interpret the coefficients in the standard form of a line?

**Tip:** Always try to eliminate fractions when converting to standard form by multiplying through by the denominator.

Write an equation of the line through (−5,−4) having slope 17/16. Give the answer in standard form.

Find the equation of the line passing through (-5, -4) with a slope of 17/16. The solution shows how to convert the point-slope form of the line into standard form (Ax + By = C) with step-by-step explanations. Suitable for students in Grades 8-10.

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