Question

What is an equation of the line that passes through the point left bracket, minus, 1, comma, 8, right bracket(−1,8) and is parallel to the line x, plus, y, equals, 3x y=3?

Answer 1

The equation of the line that passes through the point (-1, 8) and is parallel to the line y = 9 + 3x is y = 3x + 11.

Step-by-step explanation:

To find the equation of the line that passes through the point (-1, 8) and is parallel to the line y = 9 + 3x, we should note that parallel lines have the same slope. In this case, since the slope (m) is 3, our unknown line must also have a slope of 3. Using the point-slope form of a line which is y - y1 = m(x - x1), where (x1, y1) is the given point and m is the slope, we can substitute the values to find the equation of our unknown line.

Plugging in slope 3 and the coordinates of the point (-1, 8) into the point-slope form, we get:

y - 8 = 3(x - (-1))

y - 8 = 3(x + 1)

y - 8 = 3x + 3

To write it in slope-intercept form, we add 8 to both sides, resulting in:

y = 3x + 11

This is the equation of the line passing through the point (-1, 8) and parallel to the given line.