Final answer:
The question asks to match linear equations with their corresponding forms: slope-intercept form, standard form, and point-slope form. Slope-intercept form is y = a + bx, where a is the y-intercept, and b is the slope. Point-slope form is y - y1 = m(x - x1), and standard form is Ax + By = C.
Step-by-step explanation:
The question concerns matching each linear equation with the correct description given three different forms: point-slope form, standard form, and slope-intercept form. Each of these forms represents a linear equation but in different algebraic structures.
Slope-Intercept Form
In slope-intercept form, a linear equation is presented as y = a + bx, where a represents the y-intercept and b represents the slope of the line. This form is very useful for quickly identifying the slope and y-intercept from the equation.
Point-Slope Form
The point-slope form of a linear equation is written as y - y1 = m(x - x1), where m is the slope and (x1, y1) is a specific point on the line. This form is useful for writing the equation of a line when you know the slope and a single point on the line.
Standard Form
Standard form is typically written as Ax + By = C, where A, B, and C are integers, and A should be non-negative. This form is not as intuitive for identifying the slope or y-intercept but is often used for theoretical work and sometimes for defining lines in computer graphics.
Each form serves a specific purpose and can be transformed into another form using algebraic manipulation.