Solve: -4(1+p) + 3p - 10 = 5p - 2(3 - p) Solve: 3m - (5 - m) = 6m + 2(m - 4) - 1.

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Presentation transcript:

Solve: -4(1+p) + 3p - 10 = 5p - 2(3 - p) Solve: 3m - (5 - m) = 6m + 2(m - 4) - 1

Point-Slope Formula

Review Slope-Intercept Form y = mx + b Use when given slope and intercept Standard Form: Ax + By = C Always change to slope-intercept And now…

Point-Slope Form y - y 1 = m (x - x 1 ) Use when given a POINT and a SLOPE Can also use when given TWO POINTS Always change back to slope-intercept form

Point-Slope Form: y - y 1 = m (x - x 1 ) Write the point-slope form of an equation for a line that passes through (3, -2) with slope -4. Then change to slope-intercept form.

Point-Slope Form: y - y 1 = m (x - x 1 ) Write the slope-intercept form of an equation for a line that passes through (-1, 4) with slope 3

Point-Slope Form: y - y 1 = m (x - x 1 ) Write the slope-intercept form of an equation for a line that passes through (-3, -5) with slope 4/3

Same 3 Steps… 1st: Plug into formula 2nd: Distribute 3rd: Isolate “y” (add the opposite)

Using Point Slope with 2 Points One extra step…. MUST FIRST FIND THE SLOPE!!!

Point-Slope Form: Slope Formula: y - y 1 = m (x - x 1 ) Write the equation of the line that passes through the points (-1, 3) and (-3, -1) 1.2.[Plug in] [Distribute] [Isolate y]

Point-Slope Form: Slope Formula: y - y 1 = m (x - x 1 ) Write the equation of the line that passes through the points (6, 1) and (7, -4) 1.2.[Plug in] [Distribute] [Isolate y]

Point-Slope Form: Slope Formula: y - y 1 = m (x - x 1 ) Write the equation of the line that passes through the points (7, 3) and (-4, 3) 1.2.[Plug in] [Distribute] [Isolate y]

Parallel and Perpendicular Lines Parallel Lines Have the Same Slope – So m’s are equal! Perpendicular Lines have slopes that are OPPOSITE (sign) AND RECIPROCAL (flip)

Write the Equation of the Parallel Line Write the slope-intercept form of an equation of the line that passes through the given point and is parallel to the graph of each equation. (-2, 5); y = -4x + 2 STEP 1: Identify the slope m = ___ STEP 2: Identify the Parallel slope //m = ____ STEP 3: Plug POINT and Parallel slope into Point- Slope Formula and solve y – 5 = -4 (x + 2) y – 5 = -4x – 8 y = -4x – 3DONE!

Write the Equation of the Perpendicular Line Write the slope-intercept form of an equation of the line that passes through the given point and is perpendicular to the graph of each equation. (-4, -3); 4x + y = 7 STEP 1: Solve for y (to get in slope-intercept form) STEP 2: Identify the slope m = ___ STEP 3: Identify the ┴ m = ____ STEP 4: Plug POINT and PERPENDICULAR SLOPE into Point – Slope Formula and solve

Write the Equation of the Perpendicular Line Write the slope-intercept form of an equation of the line that passes through the given point and is perpendicular to the graph of each equation. (-4, -3); 4x + y = 7 y = -4x + 7 m = -4 ┴m = ¼ y + 3 = ¼ (x + 4) y + 3 = ¼ x + 1 y = ¼ x – 2