Final answer:
The equation in standard form of the line that contains the point (-1,3) and is parallel to the line y=8x-1 is y = 8x + 11.
Step-by-step explanation:
To find the equation of a line parallel to the line y=8x-1 and passing through the point (-1,3), we can use the fact that parallel lines have the same slope. The given line has a slope of 8, so the parallel line will also have a slope of 8. The equation of a line in point-slope form is y - y₁ = m(x - x₁), where (x₁, y₁) is a point on the line and m is the slope of the line.
So, we can substitute the values (-1,3) and m=8 into the equation:
y - 3 = 8(x - (-1))
Simplifying this equation gives:
y - 3 = 8(x + 1)
Expanding and rearranging terms, we get:
y - 3 = 8x + 8
y = 8x + 11
Therefore, the equation in standard form of the line parallel to y=8x-1 and passing through the point (-1,3) is y = 8x + 11.