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. through (-5,4), m = -3/2

Key Concepts

Point-Slope Form

The point-slope form of a linear equation is expressed as y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope. This form is particularly useful when you know a point on the line and the slope, allowing you to easily write the equation of the line.

Slope-Intercept Form

The slope-intercept form of a linear equation is given by y = mx + b, where m represents the slope and b is the y-intercept. This form is advantageous for quickly identifying the slope and where the line crosses the y-axis, making it easier to graph the equation.

Standard Form

The standard form of a linear equation is written 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 can be converted to slope-intercept form for graphing purposes.