Write an equation of the line passing through the given...

Write an equation of the line passing through the given point and having the given slope. Give the equation (a) in slope-intercept form and (b) in standard form. See Example 3 and the discussion on standard form.
$$
(7,-2) ; \text { slope } \frac{1}{4}
$$

Key Concepts

Standard Form

The standard form of a linear equation is typically written as Ax + By = C, where A, B, and C are integers. This form is useful for dealing with equations in contexts where integer coefficients are preferred and helps in analyzing the intercepts and overall structure of the line.

Slope-Intercept Form

The slope-intercept form, given by y = mx + b, explicitly shows the slope (m) and the y-intercept (b) of a line. This form makes it easy to graph the line and understand how changes in x affect y, which is particularly useful in many areas of algebra and calculus.

Linear Equation

A linear equation represents a straight line on the coordinate plane and reflects the relationship between two variables, typically x and y. It forms the foundation for understanding graphs and basic algebraic relationships, and its different forms can emphasize various properties of the line.

Slope

The slope is a measure of how steep a line is, indicating the ratio of the vertical change (rise) to the horizontal change (run) between any two points on the line. It is a fundamental concept in algebra, crucial for understanding the behavior and direction of a line.

Point-Slope Form

The point-slope form is a method to write the equation of a line when the slope and a specific point on the line are known. Expressed as y - y? = m(x - x?), it provides a direct way to derive the line's equation, which can then be manipulated into other forms like slope-intercept or standard form.

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