Write an equation for each line described. Give answers in standard form for Exercises 11–20 and in slope-intercept form (if possible) for Exercises 21–32. x-intercept (3,0), y-intercept (0,-2)

Key Concepts

Intercepts

Intercepts are points where a line crosses the axes on a graph. The x-intercept is the point where the line intersects the x-axis, represented as (a, 0), while the y-intercept is where it intersects the y-axis, represented as (0, b). In this case, the x-intercept is (3, 0) and the y-intercept is (0, -2), which are crucial for determining the equation of the line.

Slope-Intercept Form

The slope-intercept form of a linear equation is given by the formula y = mx + b, where m represents the slope of the line and b represents the y-intercept. This form is particularly useful for quickly identifying the slope and y-intercept, allowing for easy graphing of the line. For the given intercepts, the slope can be calculated using the coordinates of the intercepts.

Standard Form of a Linear Equation

The standard form of a linear equation is expressed as Ax + By = C, where A, B, and C are integers, and A should be non-negative. This form is useful for solving systems of equations and for understanding the relationship between the coefficients and the graph of the line. Converting from slope-intercept form to standard form may be necessary depending on the requirements of the problem.