Question

graph the equation of a line that has a slope of \\(\frac{3}{2}\\) and passes through the point (6, -2).

Explanation:

Step1: Use point - slope form

The point - slope form of a line is $y - y_1=m(x - x_1)$, where $m$ is the slope and $(x_1,y_1)$ is a point on the line. Here, $m = \frac{3}{2}$, $x_1 = 6$, and $y_1=-2$. Substitute these values into the formula:
$y-(-2)=\frac{3}{2}(x - 6)$
Simplify the left - hand side: $y + 2=\frac{3}{2}(x - 6)$

Step2: Convert to slope - intercept form

Distribute the $\frac{3}{2}$ on the right - hand side:
$y+2=\frac{3}{2}x-9$
Subtract 2 from both sides:
$y=\frac{3}{2}x-9 - 2$
$y=\frac{3}{2}x-11$

To graph the line:

1. Plot the point $(6,-2)$ (since the line passes through this point).
2. Use the slope $\frac{3}{2}$ (rise = 3, run = 2). From the point $(6,-2)$, go up 3 units and then right 2 units to get another point (for example, $(6 + 2,-2+3)=(8,1)$), or go down 3 units and left 2 units (for example, $(6-2,-2 - 3)=(4,-5)$).
3. Draw a straight line through the plotted points.

Answer:

The equation of the line is $y=\frac{3}{2}x - 11$, and the graph is drawn by plotting the point $(6,-2)$ and using the slope $\frac{3}{2}$ to find additional points and then drawing a line through them.