Write an equation of the line through 

left parenthesis negative 1 comma negative 4 right parenthesis(−1,−4) 

having slope 

StartFraction 11 Over 17 EndFraction1117. 

Give the answer in standard form.

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Part 1

The equation of the line is 

enter your response herexminus−enter your response hereyequals=enter your response here. 

To find the equation of a line, we can use the point-slope form of a line equation:

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

Where:
- \((x_1, y_1)\) is a point on the line, which in this case is \((-1, -4)\)
- \(m\) is the slope, which is given as \(\frac{11}{17}\)

### Step 1: Substitute the given values into the point-slope form

\[
y - (-4) = \frac{11}{17}(x - (-1))
\]
This simplifies to:
\[
y + 4 = \frac{11}{17}(x + 1)
\]

### Step 2: Distribute the slope on the right side

\[
y + 4 = \frac{11}{17}x + \frac{11}{17}
\]

### Step 3: Move all terms to one side to write the equation in standard form \(Ax + By = C\)

Multiply both sides by 17 to eliminate the fraction:

\[
17(y + 4) = 11x + 11
\]

This simplifies to:

\[
17y + 68 = 11x + 11
\]

### Step 4: Rearrange the equation into standard form

Move the \(x\) and constant terms to the left side:

\[
11x - 17y = 57
\]

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

\[
11x - 17y = 57
\]

Would you like more details or have any questions? Here are 5 related questions:

1. How do you convert from point-slope form to slope-intercept form?
2. What is the difference between standard form and slope-intercept form?
3. How can you verify that a given point lies on a line?
4. What are the general steps to find the slope between two points?
5. How can you graph a line given its equation in standard form?

**Tip:** When writing equations in standard form, it's helpful to clear fractions by multiplying both sides of the equation by the denominator.

Write an equation of the line through (−1,−4) having slope 11/17. Give the answer in standard form.

Learn how to find the equation of a line passing through the point (-1, -4) with a slope of 11/17. This problem explains the conversion from point-slope form to standard form, making it easy to understand key algebra concepts. Suitable for students in Grades 8-10.

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