1. Everything You Will Ever Need To Know About Linear Equations* *Whether You Wanted To Know It Or Not!

2. Definition A linear equation in slope-intercept form can be written in the form Where m represents the slope of the line and (0, b) is the y-intercept.

3. About Slope The slope of a line is its steepness or slant. Positively-sloped lines are uphill from left to right. Negatively-sloped lines are downhill from left to right. Horizontal lines have zero slope. Vertical lines have undefined slope.

4. Important Formula Given two points The slope of the line through the points is given by

5. How To Graph A Linear Equation Write the equation in slope-intercept form. Graph the y-intercept (0, b) Use the slope m to “rise” and “run” from the y-intercept to another point on the graph.

6. About Horizontal and Vertical Lines The equation of every horizontal line is y = k, where k is some number. Horizontal lines have zero slope. The equation of every vertical line is x = h, where h is some number. Vertical lines have undefined slope.

7. About Parallel and Perpendicular Lines If two lines in the plane are parallel (do not intersect), the lines have equal slopes. If two lines in the plane are perpendicular (meet at a 90-degree angle), the lines have “opposite-reciprocal” slopes.

8. How To Find The Equation of a Line If you are given the slope of the line and a point on the line, use point-slope form:

9. How to Find the Equation of a Line (continued) If you are given two points on the line, use the slope formula to find the slope of the line. Then use point-slope form.

10. How to Find the Equation of a Line (continued) If you are told that your line is parallel or perpendicular to a given line, find the slope of that line. If the lines are parallel, use that slope. If the lines are perpendicular, use the opposite reciprocal of that slope. Use point-slope form to find your equation.

11. Example Find the equation for the line containing the points (4, 2) and (3, 6). Answer: y – 2 = -4(x – 4) Or: y – 6 = -4(x – 3)