Question

Find an equation of the line, in point slope form, through the point (7, 4), and parallel to the line 3x-y=-2

Answer 1

To find the equation of the line in point-slope form that goes through the point (7, 4) and is parallel to the line given by the equation \(3x - y = -2\), we first need to determine the slope of the given line.

1. **Convert the line to slope-intercept form (y = mx + b)**:
\[
3x - y = -2
\]
Rearranging this equation, we get:
\[
-y = -3x - 2
\]
Multiplying by -1, we obtain:
\[
y = 3x + 2
\]

From this, we see that the slope (\(m\)) of the line is 3.

2. **Since parallel lines have the same slope**, the slope of our new line will also be 3.

3. **Using the point-slope form of the equation of a line**, which is given by:
\[
y - y_1 = m(x - x_1)
\]
where \((x_1, y_1)\) is the point through which the line passes. Plugging in \(m = 3\) and the point \((7, 4)\) into the equation, we have:
\[
y - 4 = 3(x - 7)
\]

Therefore, the equation of the line in point-slope form is:
\[
y - 4 = 3(x - 7)
\]