For each line described, write an equation in(a)slope-intercept form, if possible, and(b)standard form. through (-2, 4) and (1, 3)

Key Concepts

Slope-Intercept Form

The slope-intercept form of a linear equation is expressed as y = mx + b, where m represents the slope of the line and b is the y-intercept. This form is useful for quickly identifying the slope and y-intercept, making it easier to graph the line. To convert a line through two points into this form, one must first calculate the slope and then use one of the points to find the y-intercept.

Standard Form

The standard form of a linear equation is given as Ax + By = C, where A, B, and C are integers, and A should be non-negative. This form is particularly useful for solving systems of equations and for easily identifying intercepts. To convert from slope-intercept form to standard form, one rearranges the equation to fit this format, often requiring multiplication to eliminate fractions.

Finding the Slope

The slope of a line measures its steepness and direction, calculated as the change in y divided by the change in x (rise over run) between two points. For points (x1, y1) and (x2, y2), the slope m is given by m = (y2 - y1) / (x2 - x1). Understanding how to find the slope is essential for writing the equation of a line, as it directly influences both the slope-intercept and standard forms.