write the equation of a line that is parallel to y=4x+5 and passes through the point 7,2 in point slope form

Answer 1

To find the equation of a line parallel to y=4x+5 and passing through the point (7,2), we can use the point-slope form of a linear equation.

The equation of a line in point-slope form is given by: y - y₁ = m(x - x₁)

Where:
- (x₁, y₁) are the coordinates of the given point (7,2)
- m is the slope of the line we are looking for

Since the line we want is parallel to y=4x+5, it will have the same slope. Therefore, the slope we need to use is 4.

Plugging in the values into the point-slope form equation, we have:

y - 2 = 4(x - 7)

Simplifying further:

y - 2 = 4x - 28

Now, let's rearrange the equation to obtain the slope-intercept form (y = mx + b):

y = 4x - 28 + 2

This simplifies to:

y = 4x - 26

Therefore, the equation of the line parallel to y=4x+5 and passing through the point (7,2) in point-slope form is y - 2 = 4(x - 7).