write an equation for the line that is parallel to the given line and passes throught the given point y=3x+7;(2,10)
To find an equation for the line that is parallel to y = 3x + 7 and passes through the point (2,10), we can use the point-slope form of a linear equation.
The given line y = 3x + 7 has a slope of 3. Since the line we are trying to find is parallel, it will also have a slope of 3.
Using the point-slope form, we have:
y - y1 = m(x - x1)
where m represents the slope, (x1, y1) represents the given point.
Plugging in the values, we get:
y - 10 = 3(x - 2)
Expanding the equation, we have:
y - 10 = 3x - 6
Now, let's isolate y:
y = 3x - 6 + 10
Simplifying further:
y = 3x + 4
Therefore, the equation of the line parallel to y = 3x + 7 and passing through the point (2,10) is y = 3x + 4.