Algebra 1 ~ Sections 5-4 & 5-5 & Standard Form Writing Equations of Lines in Point-Slope Form, Slope-Intercept Form, and Standard Form

In Lesson 5-3, you saw that if you know the slope of a line and the y-intercept, you can graph the line. You can also graph a line if you know its slope and any point on the line.

The equation of the line that is generated using the coordinates of a known point and the slope of the line is known as point-slope form.

Ex. 1 Write the linear equation in: a) Point-Slope Form. b) Slope-Intercept Form. c) Then identify the slope and y-intercept. slope = 2; (3, 1) y – y 1 = m(x – x 1 ) y – (1) = 2(x – (3)) P.S. F. y – 1 = 2(x - 3) y – 1 = 2(x - 3) y – 1 = 2x – 6 S. I. F. y = 2x – 5 Slope: 2 y-int = -5

slope = ½ ; (-4, 3) y – y 1 = m(x – x 1 ) y – (3) = ½ (x – (-4)) P.S. F. y – 3 = ½ (x + 4) y – 3 = ½ (x + 4) y – 3 = ½ x + 2 S. I. F. y = ½ x +5 Slope: ½ y-int = 5 Ex. 2 Write the linear equation in: a) Point-Slope Form. b) Slope-Intercept Form. c) Then identify the slope and y-intercept.

Ex. 3 Write the linear equation in: a) Point-Slope Form. b) Slope-Intercept Form. c) Then identify the slope and y-intercept. slope = 1/3 ; (-3, 1) y – y 1 = m(x – x 1 ) y – (1) = 1/3(x – (-3)) P.S. F. y – 1 = 1/3(x + 3) y – 1 = 1/3(x + 3) y – 1 = 1/3x + 1 S. I. F. y = 1/3x + 2 Slope: 1/3 y-int = 2

Ex. 4 – What was the given slope and the ordered pair that was given to generate the Point-Slope Formula below. y – 4 = 3(x + 1) Slope is 3 Order Pair (-1, 4)

Ex. 5 – What was the given slope and the ordered pair that was given to generate the Point-Slope Formula below. y + 2 = –5(x – 7) Slope is -5 Order Pair (7, -2)

Ex. 6 Write an equation in slope-intercept form for the line that passes through the points (-1, 6) and (7, -10). Then identify the slope and y-intercept. (-1, 6) and (7, -10) y – y 1 = m(x – x 1 ) y – (6) = -2(x – (-1)) P.S. F. y – 6 = -2(x + 1) y – 6 = -2(x + 1) y – 6 = -2x – 2 S. I. F. y = -2x + 4 Slope: -2 y-int = 4 m = –2, Now pick one of the given points. m = –2 and (-1, 6)

Ex. 6 cont. Write an equation in slope- intercept form for the line that passes through the points (-1, 6) and (7, -10). Then identify the slope and y-intercept. (-1, 6) and (7, -10) y – y 1 = m(x – x 1 ) y – (-10) = -2(x – (7)) P.S. F. y + 10 = -2(x – 7) y + 10 = -2(x – 7) y +10 = -2x +14 S. I. F. y = -2x + 4 Slope: -2 y-int = 4 m = –2, Now pick one of the given points. m = –2 and (7, -10)

Ex. 7 Write an equation in slope-intercept form for the line that passes through the points (6, -25) and (-1, 3). Then identify the slope and y-intercept. (6, -25) and (-1, 3) y – y 1 = m(x – x 1 ) y – (-25) = -4(x –(6)) P.S. F. y + 25 = -4(x – 6) y +25 = -4(x – 6) y + 25 = -4x +24 S. I. F. y = -4x – 1 Slope: -4 y-int = 1 m = –4, Now pick one of the given points. m = –4 and (6, -25)

Ex. 7 Cont. Write an equation in slope- intercept form for the line that passes through the points (6, -25) and (-1, 3). Then identify the slope and y-intercept. (6, -25) and (-1, 3) y – y 1 = m(x – x 1 ) y – (3) = -4(x –(-1)) P.S. F. y – 3 = -4(x + 1) y – 3 = -4(x + 1) y - 3 = -4x – 4 S. I. F. y = -4x – 1 Slope: -4 y-int = 1 m = –4, Now pick one of the given points. m = –4 and (-1, 3)

Ex. 8 Write an equation in slope-intercept form for the line that passes through the points (10, -1) and (4, 2). Then identify the slope and y-intercept. (10, -1) and (4, 2) y – y 1 = m(x – x 1 ) y – (2) = -½(x – (4)) P.S. F. y – 2 = -½(x – 4) y – 2 = -½(x – 4) y – 2 = -½x + 2 S. I. F. y = -½ x + 4 Slope: -½ y-int = 4 m = -½, Now pick one of the given points. m = –½ and (4, 2)

Ex. 8 Cont. Write an equation in slope- intercept form for the line that passes through the points (10, -1) and (4, 2). Then identify the slope and y-intercept. (10, -1) and (4, 2) y – y 1 = m(x – x 1 ) y – (-1) = -½(x – (10)) P.S. F. y + 1 = -½(x – 10) y + 1 = -½(x – 10) y +1 = -½x + 5 S. I. F. y = -½ x + 4 Slope: -½ y-int = 4 m = -½, Now pick one of the given points. m = –½ and (10, -1)

Forms of Linear Equations Point – Slope Form y – y 1 = m(x – x 1 ) Slope – Intercept Form y = mx + b Standard Form Ax + By = C  A has to be POSITIVE!!!  A, B and C can not be FRACTIONS or DECIMALS, only INTEGERS!!!  A and B can not BOTH be zero. You must know these equations!!!

Ex. 9 - Write the equation in standard form (Ax + By = C) y – 5 = 4(x + 2) y – 5 = 4x y = 4x + 13 − 4x − 4x + y = 13 4x – y = − 13

Ex Write the equation in standard form (Ax + By = C) P.S. F. y – 3 = ½(x – 4) y – 3 = ½(x – 4) y – 3 = ½x – 2 S. I. F. y = ½ x + 1 Slope: ½ y-int = 1 S. T. F. x - 2y = -2

Ex. 11 – Write the equation of the line that passes through (3, 4) and has a slope of -2. A.) in point-slope form B.) in slope-intercept form C.) in standard form P.S. F. y – 2 = – 2(x – 3) P.S. F. y = –2x +8 S.T. F. 2x + y = 8

Assignment Pages #’s 4-7, 11-15, 19-23, Parts a) Point-Slope Form b) Slope-Intercept Form c) Identify the slope and y-intercept d) Standard Form