Question

1. slope = -1, through (3, 0)
2. slope = 0, through (4, -2)

Explanation:

Problem 7 (slope = -1, through (3, 0))

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, $m=-1$, $x_1 = 3$, and $y_1=0$.

Step2: Substitute values into the formula

Substitute $m=-1$, $x_1 = 3$, and $y_1 = 0$ into $y - y_1=m(x - x_1)$:
$y-0=-1(x - 3)$

Step3: Simplify the equation

Simplify the right - hand side: $y=-x + 3$. To graph this line, we know that the y - intercept is 3 (when $x = 0$, $y=3$) and the slope is - 1, which means for every 1 unit we move to the right along the x - axis, we move 1 unit down along the y - axis. We can also plot the point (3,0) and use the slope to find other points.

Problem 8 (slope = 0, through (4, -2))

Step1: Recall the equation of a horizontal line

A line with a slope of 0 is a horizontal line. The equation of a horizontal line is of the form $y = k$, where $k$ is the y - coordinate of any point on the line.

Step2: Determine the value of k

Since the line passes through the point (4, - 2), the y - coordinate of this point is - 2. So the equation of the line is $y=-2$. To graph this line, we draw a horizontal line that passes through all points with a y - coordinate of - 2. For example, the point (4, - 2) is on the line, and other points like (0, - 2), (1, - 2), etc., are also on the line.

For Problem 7:

Answer:

The equation of the line is $y=-x + 3$

For Problem 8: