Find an equation of the line that satisfies the given conditions. through \( (3,2) \); slope 2

To find the equation of the line that goes through the point \( (3,2) \) with a slope of \( 2 \), you can use the point-slope form of the equation of a line, which is given by: \[ y - y_1 = m(x - x_1) \] Here, \( m \) is the slope, and \( (x_1, y_1) \) is the point the line passes through. Plugging in the values we have: \[ y - 2 = 2(x - 3) \] Now, simplify this equation: \[ y - 2 = 2x - 6 \] \[ y = 2x - 4 \] So the equation of the line is \( y = 2x - 4 \). When it comes to slope-intercept form, which is \( y = mx + b \), the \( b \) value is the y-intercept. In our equation, by rearranging, we can see that when \( x = 0 \), \( y = -4 \), so the line crosses the y-axis at \( (0, -4) \). Understanding this can help visualize the graph of the line! Now, it's key to remember that when you're concentrating on slope and points, don’t forget to check your calculations! A common mistake is switching the x and y coordinates, leading to a completely different line equation. Always double-check your point inputs to avoid this.