For each line described, write an equation in(a)slope-intercept form, if possible, and(b)standard form. through (3, -5) with slope -2.

Key Concepts

Slope-Intercept Form

The slope-intercept form of a linear equation is expressed as y = mx + b, where m represents the slope and b is the y-intercept. This form is useful for quickly identifying the slope of the line and where it crosses the y-axis. To convert a point and slope into this form, you can substitute the point's coordinates into the equation and solve for b.

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 beneficial for analyzing the relationship between x and y in a more general way. To convert from slope-intercept form to standard form, you rearrange the equation to isolate the variables on one side.

Point-Slope Form

The point-slope form of a linear equation is written as y - y1 = m(x - x1), where (x1, y1) is a specific 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, as it allows for easy conversion to slope-intercept or standard form. In this case, you can directly apply the given point (3, -5) and slope (-2) to formulate the equation.