Write an equation for the line that is parallel to the given line that passes through the given point.

y=3x+7; (2,10)

slope = m = 3

10 = 3 (2) + b

b = 4

y = 3 x + 4

To find the equation of a line that is parallel to a given line and passes through a given point, we need to use the concept of the slope.

The given line has the equation: y = 3x + 7.

To determine the slope of this line, we can compare it to the standard slope-intercept form, y = mx + b, where m represents the slope. In this case, the slope (m) of the given line is 3.

Since parallel lines have the same slope, our new line must also have a slope of 3.

Now, let's use this information, along with the given point (2,10), to find the equation of the line.

We can substitute the coordinates (x, y) of the given point and the slope (m) into the point-slope form equation: y - y1 = m(x - x1).

Substituting in the values, we get: y - 10 = 3(x - 2).

Next, distribute the 3: y - 10 = 3x - 6.

Now, we isolate y by adding 10 to both sides: y = 3x - 6 + 10.

Simplifying, we have y = 3x + 4.

Therefore, the equation of the line that is parallel to y = 3x + 7 and passes through the point (2,10) is y = 3x + 4.