Question

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

Answer 1

The equation of the line that passes through the point $(-1,-4)$ and is parallel to the line $7x+y=7$ can be found by using the slope-intercept form of a line, which is:

$y = mx + b$

where $m$ is the slope (which is the same for both lines) and $b$ is the $y$-intercept (which is the $y$-value of the point where the line passes through).

Since the given line is $7x+y=7$, we can see that the slope is $7$. Therefore, the slope of the line that passes through the point $(-1,-4)$ and is parallel to the given line is also $7$.

Now, we need to find the $y$-intercept of the line. To do this, we can substitute the values of $x$ and $y$ from the point $(-1,-4)$ into the slope-intercept form of the line:

$y = mx + b$

$y = 7(-1) + b$

$y = -7 + b$

$b = -7$

Therefore, the equation of the line that passes through the point $(-1,-4)$ and is parallel to the line $7x+y=7$ is:

$y = 7x - 7$

Explanation: