Question

write an equation for the line that is parallel to the given line and passes throught the given point y=3x+7;(2,10)

Answer 1

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.