Writing Linear Equations from Ordered Pairs Algebra 1

Learning Targets Write an equation in slope-intercept form from a slope and point Write an equation in slope-intercept form from two points Write an equation in point-slope form from a slope and point Write an equation in point-slope form from two points

Writing Linear Equations: Example 1 Point Slope (slope/point) Write an equation of a line, in point-slope form, with a slope of 1 4 and through the point (3, −2). 𝑦− 𝑦 1 =𝑚 𝑥− 𝑥 1 𝑦+2= 1 4 (𝑥−3)

Writing Linear Equations: Example 2 Point Slope (slope/point) Write an equation of a line, in point-slope form, with a slope of − 7 4 and through an x-intercept of −9. 𝑦− 𝑦 1 =𝑚 𝑥− 𝑥 1 x-intercept: (−9, 0) 𝑦−0=− 7 4 𝑥+9 𝑦=− 7 4 (𝑥+9)

Writing Linear Equations: Example 3 Point Slope (slope/point) Write an equation of a line, in point-slope form, with a slope of 4 3 and through the point (7, 2). 𝑦− 𝑦 1 =𝑚 𝑥− 𝑥 1 𝑦−2= 4 3 (𝑥−7)

Writing Linear Equations: Example 1 Slope Intercept (slope/point) Write an equation of a line, in slope-intercept form, with a slope of 4 5 and through the point (0, 2). Start in point slope and isolate y to transform into slope intercept 𝑦−2= 4 5 (𝑥−0) 𝑦−2= 4 5 𝑥 𝑦= 4 5 𝑥+2

Writing Linear Equations: Example 2 Slope Intercept (slope/point) Write an equation of a line, in slope-intercept form, with a slope of −3 and through the point (1, −2). 𝑦+2=−3(𝑥−1) 𝑦+2=−3𝑥+3 𝑦=−3𝑥+1

Writing Linear Equations: Example 3 Slope Intercept (slope/point) Write an equation of a line, in slope-intercept form, with a slope of −2 and through the point (−3, 0). 𝑦−0=−2(𝑥+3) 𝑦=−2𝑥−6

Writing Linear Equations: Example 1 Point Slope (2 points) Write an equation of a line, in point slope form, through the points 2, 4 and (−1, −3). 𝑦− 𝑦 1 =𝑚 𝑥− 𝑥 1 𝑚= −3−4 −1−2 =− −7 −3 = 7 3 2 options 𝑦+3= 7 3 (𝑥+1) or 𝑦−4= 7 3 (𝑥−2)

Writing Linear Equations: Example 2 Point Slope (2 points) Write an equation of a line, in point-slope form, through the points (−8, 0) and (5, −1). 𝑦− 𝑦 1 =𝑚 𝑥− 𝑥 1 𝑚= −1−0 5−−8 =− 1 13 2 options 𝑦−0=− 1 13 (𝑥+8) or 𝑦+1=− 1 13 (𝑥−5)

Writing Linear Equations: Example 3 Point Slope (2 points) Write an equation of a line, in point-slope form, through the points (3, 1) and (2, 4). 𝑦− 𝑦 1 =𝑚 𝑥− 𝑥 1 𝑚= 4−1 2−3 = 3 −1 =−3 2 options 𝑦−1=−3(𝑥−3) or 𝑦−4=−3(𝑥−2)

Writing Linear Equations: Example 1 Slope Intercept (2 points) Write an equation of a line, in slope-intercept form, through the points (−4, 1) and (0, 2). 𝑚= 2−1 0−−4 = 1 4 𝑦−2= 1 4 (𝑥−0) 𝑦−2= 1 4 𝑥 𝑦= 1 4 𝑥+2

Writing Linear Equations: Example 2 Slope Intercept (2 points) Write an equation of a line, in slope-intercept form, through an x-intercept of (−3, 0) and a y-intercept of (0, 6). 𝑚= 6−0 0−−3 = 6 3 =2 𝑦−0=2(𝑥+3) 𝑦=2𝑥+6

Writing Linear Equations: Example 3 Slope Intercept (2 points) Write an equation of a line, in slope-intercept form, through the points (2, 2) and (−9, 6). 𝑚= 6−2 −9−2 = 4 −11 𝑦−2=− 4 11 𝑥−2 𝑦−2=− 4 11 𝑥+ 8 11 𝑦=− 4 11 𝑥+ 38 11