Find the general form of the equation of the line that...

Find the general form of the equation of the line that passes through the given point and has the indicated slope. Sketch the line by hand. Use a graphing utility to verify your sketch, if possible.
Point $\quad$ Slope
$(2.3,-8.5) \quad m=0$

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Key Concepts

Line Equations

A line in the plane can be described using various forms including the slope-intercept form, the point-slope form, and the general form. The general form, usually written as Ax + By + C = 0, presents the line in a standard algebraic format that is useful for identifying properties such as intercepts and for performing further algebraic analyses.

Slope

The slope of a line measures its steepness and indicates its direction. It is defined as the ratio of the vertical change to the horizontal change between any two points on the line. When a line has a slope of zero, it means there is no vertical change as the horizontal coordinate varies, resulting in a horizontal line.

Point-Slope Form

The point-slope form is a method to write the equation of a line when a specific point and the slope are known. It uses the formula y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope. This form is especially useful for quickly formulating an equation before converting it into other forms such as the general form.

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