A line intersects the points $$ (1,7) $$ and $$ (2,10) $$. $$ m=3 $$

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To find the equation of the line that intersects the points $$ (1, 7) $$ and $$ (2, 10) $$ with a slope $$ m = 3 $$, we can use the point-slope form of the equation of a line, which is given by:

$$
y - y_1 = m(x - x_1)
$$

We can use either of the two points. Let's use the point $$ (1, 7) $$.

Substituting $$ m = 3 $$, $$ x_1 = 1 $$, and $$ y_1 = 7 $$ into the equation, we get:

$$
y - 7 = 3(x - 1)
$$

Now, we can simplify this equation:

$$
y - 7 = 3x - 3
$$

Adding 7 to both sides:

$$
y = 3x + 4
$$

Now, let's check if this line passes through the second point $$ (2, 10) $$:

Substituting $$ x = 2 $$ into the equation:

$$
y = 3(2) + 4 = 6 + 4 = 10
$$

Since the calculated $$ y $$ value matches the second point, the equation of the line is confirmed to be:

$$
\boxed{y = 3x + 4}
$$
The equation of the line is $$ y = 3x + 4 $$.

A line intersects the points
and .

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A line intersects the points and .