Linear Functions: Slopes, Equations, and Graphs

Study Notes

The text is about solving problems related to linear functions, specifically calculating slopes, finding equations in different forms, and graphing lines.
To find the slope between two points (x1, y1) and (x2, y2), use the formula: (y2 - y1) / (x2 - x1).
In the equation y = mx + b, m is the slope and b is the y-intercept.
To graph equations in different forms, use specific methods: vertical lines (x = a), horizontal lines (y = b), slope-intercept form (y = mx + b), and point-slope form (y - y1 = m(x - x1)).
To graph an equation in standard form (Ax + By = C), use the intercepts: x-intercept (replace y with 0 and solve for x) and y-intercept (replace x with 0 and solve for y).
To write the equation of a line passing through a point (x1, y1) with a given slope m, use the point-slope formula (y - y1 = m(x - x1)).
To find the equation of a line passing through two points (x1, y1) and (x2, y2), calculate the slope first (y2 - y1 / x2 - x1) and then use the point-slope formula (y - y1 = m(x - x1)).
Parallel lines have the same slope, and perpendicular lines have negative reciprocal slopes.
To write the equation of a line passing through a point and parallel to a given line, use the slope of the given line and the point-slope formula.
To write the equation of a line passing through a point and perpendicular to a given line, use the negative reciprocal of the slope of the given line and the point-slope formula.