Question

1. slope = \\(\frac{3}{4}\\), through (3, 0)

Explanation:

Step1: Recall point - slope form

The point - slope form of a linear equation 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, $m = \frac{3}{4}$ and $(x_1,y_1)=(3,0)$.
Substitute these values into the point - slope form: $y - 0=\frac{3}{4}(x - 3)$.

Step2: Simplify the equation

Simplify the left - hand side and the right - hand side of the equation. The left - hand side $y - 0$ is just $y$, and the right - hand side $\frac{3}{4}(x - 3)=\frac{3}{4}x-\frac{9}{4}$. So the equation of the line is $y=\frac{3}{4}x-\frac{9}{4}$.
To graph the line:

• Start with the point $(3,0)$ (the given point).
• Use the slope $\frac{3}{4}$, which means from the point $(3,0)$, move up 3 units (since the numerator of the slope is 3) and then move to the right 4 units (since the denominator of the slope is 4) to get the next point $(3 + 4,0+3)=(7,3)$.
• You can also move down 3 units and to the left 4 units from the point $(3,0)$ to get the point $(3-4,0 - 3)=(-1,-3)$.
• Then draw a straight line through these points.

Answer:

The equation of the line is $y=\frac{3}{4}x-\frac{9}{4}$ (and the graph can be drawn using the point $(3,0)$ and the slope to find other points as described above).