Final answer:
The equation of the line that passes through the point (-1,0) and is parallel to the line 5x + y = 6 is y = -5x - 5. This is obtained by finding the slope of the given line, which is -5, and applying it to the point-slope form with the given point (-1,0).
Step-by-step explanation:
To find the equation of the line that passes through the point (-1,0) and is parallel to the line 5x + y = 6, first, we need to determine the slope of the given line. The slope-intercept form of a line is y = mx + b, where m is the slope. To get the slope of the given line, we rewrite it in slope-intercept form:
5x + y = 6
y = -5x + 6
Here, the slope (m) is -5. For two lines to be parallel, they must have the same slope. Therefore, the slope of our desired line is also -5.
Now, we use the point-slope form of a line, which is y - y1 = m(x - x1), where (x1, y1) is the point the line passes through, and m is the slope. Substituting the point (-1,0) and the slope -5:
y - 0 = -5(x - (-1))
y = -5x - 5
This is the equation of the line that passes through (-1,0) and is parallel to 5x + y = 6.