Question

1. slope = -1, 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, $m=- 1$ and $(x_1,y_1)=(3,0)$.
Substitute these values into the point - slope form: $y - 0=-1(x - 3)$.

Step2: Simplify the equation

Simplify the equation $y - 0=-1(x - 3)$ to get $y=-x + 3$.
To graph the line:

• Start by plotting the point $(3,0)$ on the coordinate plane.
• The slope $m=-1=\frac{-1}{1}$, which means for every 1 unit we move to the right (increase in $x$ by 1), we move down 1 unit (decrease in $y$ by 1). So from $(3,0)$, moving right 1 unit and down 1 unit gives the point $(4,-1)$; moving left 1 unit and up 1 unit from $(3,0)$ gives the point $(2,1)$.
• Draw a straight line passing through these points.

Answer:

The equation of the line is $y=-x + 3$, and the graph is a straight line passing through the points $(3,0)$, $(2,1)$, $(4,-1)$ etc. (with the correct line drawn on the given coordinate grid).