Question

Write the slope-intercept form of the equation of the line passing through the point (0.5, -1) and parallel to the line y = 4x - 1.

Options:
a. y = 4x - 3.5,
b. y = 4x + 1.5,
c. y = 4x - 2,
d. y = 4x - 1

Answer 1

The slope-intercept form of the equation of the line passing through the point (0.5, -1) and parallel to y = 4x - 1 is y = 4x - 3.

Step-by-step explanation:

To find the equation of the line passing through the point (0.5, -1) and parallel to the line y = 4x - 1, we can use the fact that parallel lines have the same slope. Since the given line has a slope of 4, the parallel line will also have a slope of 4. Using the point-slope form of a linear equation, we can write the equation as:

y - y1 = m(x - x1)

where (x1, y1) is the given point and m is the slope. Plugging in the values, we get:

y - (-1) = 4(x - 0.5)

Simplifying, we have:

y + 1 = 4x - 2

y = 4x - 3

Hence, the slope-intercept form of the equation of the line passing through the point (0.5, -1) and parallel to the line y = 4x - 1 is y = 4x - 3.