Sketch by hand the graph of the line passing through the given point and having the given slope.

step 1 draw a line passing through the point minus 2 comma 8 and slope is equal to minus 1. So minus 2

Sketch by hand the graph of the line passing through the...

Key Concepts

Slope

The slope of a line describes how steep the line is and the direction in which it tilts. It is calculated as the ratio of the vertical change to the horizontal change between two points on the line. A negative slope, as given in the problem, indicates that the line falls as it moves from left to right.

Point-Slope Form

The point-slope form is a way of expressing the equation of a line when you know one point on the line and its slope. It is written as y - y? = m(x - x?), where (x?, y?) represents the known point and m is the slope. This form is useful for quickly writing the equation of a line from given information.

Graphing Linear Equations

Graphing a linear equation involves plotting the line on a coordinate plane. This is typically done by using the equation of the line to find at least two points, which are then connected with a straight line. Labeling points and clearly marking the coordinates enhances understanding and ensures accuracy when visualizing the line.

Selecting and Labeling Two Points

To accurately depict a line on a graph, it's important to select at least two distinct points that lie on the line. These points can be found by substituting different x-values into the line's equation or by applying the slope from a known point. Labeling these points on the graph helps in both verifying the correctness of the graph and in communicating the solution clearly.

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