Finding the Slope-Intercept Form In Exercises 51-60, write...

Finding the Slope-Intercept Form In Exercises 51-60, write an equation of the line that passes through the points. Use the slope-intercept form (if possible). If not possible, explain why and use the general form. Use a graphing utility to graph the line (if possible). $(1,1),\left(6,-\frac{2}{3}\right)$

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Key Concepts

Point-Slope Form

The point-slope form, expressed as y - y? = m(x - x?), is used to formulate the equation of a line when one point on the line and the slope are known. It serves as an intermediate representation that can be manipulated to yield the slope-intercept form.

Y-Intercept

The y-intercept is the point at which a line crosses the y-axis. In the context of a linear equation written in slope-intercept form, it is represented by the constant term, indicating the value of y when x is zero.

Slope-Intercept Form

The slope-intercept form of a linear equation is written as y = mx + b, where m is the slope and b is the y-intercept. This form is particularly useful because it immediately shows both the slope of the line and where it intersects the y-axis.

Linear Equation

A linear equation represents a straight line in the coordinate plane and is generally expressed in forms that highlight its slope and intercepts. It is a fundamental concept in algebra and is used to model constant rate situations.

Slope

The slope is a measure of the steepness and direction of a line. It is calculated by taking the difference in the y-values divided by the difference in the x-values between any two points on the line, representing how much the y-coordinate changes for a unit change in the x-coordinate.

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