7. Write an equation of the line that passes through (2, -1) and is parallel to the graph of y = 5x – 2. Write your final equation in slope-intercept form.

Answer 1

Two lines are parallel if they have the same slope. The equation y=5x-2 is already in slope-intercept form (y=mx+b), where the slope (m) is 5.

So, the line parallel to y=5x-2 will also have a slope of 5.

To find the equation of the line that passes through (2, -1) and has a slope of 5, we can use the point-slope form of a linear equation:

y - y1 = m(x - x1)

where (x1, y1) is the given point and m is the given slope.

Plugging in the values, we get:

y - (-1) = 5(x - 2)

Simplifying the equation, we have:

y + 1 = 5x - 10

Subtracting 1 from both sides, we get:

y = 5x - 11

Therefore, the equation of the line that passes through (2, -1) and is parallel to the graph of y=5x-2 is y = 5x - 11.