Using SlopeIntercept Form to Find an Equation of

Using Slope-Intercept Form to Find an Equation of a Line Use slope-intercept form to find an equation of the line with slope – 3 and passing through the point (1, − 4). Solution: y = mx + b solve for b by replacing m, x, y y = − 3 x + b (1, − 4) − 4 = − 3(1) + b − 4 = − 3 + b − 1 = b Now using both m and b, y = − 3 x − 1.

The Point-Slope Formula The point-slope formula is given by where m is the slope of the line and Note:

Using the Point-Slope Formula to Find an Equation of a Line Use the point-slope formula to find an equation of the line having a slope of − 3 and passing through the point (1, − 4). Write the answer in slope-intercept form. Solution: y y − + + = (− 4) = − 3(x − 1) 4 = − 3 x + 3 − 3 x − 1 You may use this method or the slope-intercept method for any problem, whichever you prefer.

Finding an Equation of a Line Given Two Points Find an equation of the line passing through the points (5, − 1) and (3, 1). Write the answer in slope-intercept form. Solution: First calculate the slope y − 1 = − 1(x − 3) y − 1 = −x + 3 y = −x + 4 Once you have slope, use either the point-slope or slope-intercept method to find the equation.

Find an Equation of a Line Parallel to Another Line Find an equation of the line passing through the point (– 2, – 3) and parallel to the line 4 x + y = 8. Write the answer in slope-intercept form. Solution: 4 x + y = 8 y = − 4 x + 8 First calculate the slope m = − 4 y − (− 3) = − 4[x − (− 2)] y + 3 = − 4(x + 2) Once you have slope, use either the point-slope or slope-intercept method to find the equation.

Finding an Equation of a Line Parallel to Another Line y + 3 = − 4 x − 8 y = − 4 x − 11

Find an Equation of a Line Perpendicular to Another Line Find an equation of the line passing through the point (4, 3) and perpendicular to the line 2 x + 3 y = 3. Write the answer in slope-intercept form. Solution: 2 x + 3 y = 3 Solve for y, so we can determine the slope 3 y = − 2 x + 3

Example 8: Finding an Equation of a Line Perpendicular to Another Line (2 of 3) The slope of a line perpendicular to this line must be Once you have slope, use either the point-slope or slope-intercept method to find the equation.

Finding an Equation of a Line Find an equation of the line passing through the point (− 4, 1) and perpendicular to the x-axis. Solution: Any line perpendicular to the x-axis must be vertical. x=k x = − 4

Equations of a Line: A Summary Form Standard Form Ax + By = C Example 2 x + 3 y = 6 Comments A and B must not both be zero. Prefer A positive and no fractions Horizontal Line y=k (k is constant) y=3 Vertical Line x=k (k is constant) x = − 2 The slope is undefined, and the x – intercept is (k, 0). y = − 2 x + 5 Slope = − 2 y–intercept is (0, 5). Solving a linear equation for y results in slope–intercept form. The coefficient of the x–term is the slope, and the constant defines the location of the y–intercept. Slope–Intercept Form y = mx + b Slope is m y – intercept is (0, b) The slope is zero, and the y– intercept is (0, k).

Equations of a Line: A Summary