write the equation of a line that is parallel to y=4x+5 and passes through the point 7,2 in point slope form
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).
To find the equation of a line that is parallel to the line y = 4x + 5 and passes through the point (7, 2) in point-slope form, we can use the fact that parallel lines have the same slope.
The given line y = 4x + 5 is in slope-intercept form (y = mx + b), where m represents the slope. As per the equation, the slope of this line is 4.
Since the line we are looking for is parallel to the given line, it will also have a slope of 4.
Using the point-slope form y - y1 = m(x - x1), where (x1, y1) is the given point (7, 2), and m is the slope (4), we can substitute the values and obtain the equation:
y - 2 = 4(x - 7)
This equation is in point-slope form and can be simplified further if necessary.