What is an equation of the line that passes through the point left parenthesis, minus, 1, comma, minus, 4, right parenthesis(−1,−4) and is parallel to the line x, plus, y, equals, 7x+y=7?

The equation of a line that is parallel to another line will have the same slope. 

First, let's rewrite the equation of the given line \( x + y = 7 \) in slope-intercept form, \( y = mx + b \), where \( m \) is the slope:

\[
x + y = 7 \quad \text{(subtract } x \text{ from both sides)}
\]
\[
y = -x + 7
\]

From this equation, we can see that the slope \( m \) of the line is \( -1 \).

Now, since we want the equation of a line parallel to this one, the slope of our new line will also be \( m = -1 \).

Next, we use the point-slope form of a line, which is given by:

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

Here, \( (x_1, y_1) = (-1, -4) \) is the point through which the line passes, and \( m = -1 \). Plugging these values into the equation:

\[
y - (-4) = -1(x - (-1))
\]
\[
y + 4 = -1(x + 1)
\]
\[
y + 4 = -x - 1
\]
\[
y = -x - 1 - 4
\]
\[
y = -x - 5
\]

Thus, the equation of the line is:

\[
y = -x - 5
\]

Would you like further details or have any questions?

Here are five related questions you can explore:
1. How do you convert a line from standard form to slope-intercept form?
2. What is the point-slope form of a line, and when is it useful?
3. How do you find the slope of a line given two points?
4. What does it mean for two lines to be parallel?
5. How can you find the equation of a line perpendicular to a given line?

**Tip:** The slope-intercept form, \( y = mx + b \), is often the easiest way to graph a line since it directly gives the slope and the y-intercept.

What is an equation of the line that passes through the point (−1,−4) and is parallel to the line x + y = 7?

Discover how to find the equation of a line parallel to x + y = 7 and passing through the point (−1,−4). This algebraic problem involves converting a line to slope-intercept form, using the point-slope formula, and identifying parallel line properties. Suitable for Grades 8-10 students.

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