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Linear Equations Slope-Intercept Form • Standard-form – an equation of a line in the form Ax + By + C • Value of A is greater than or equal to 0 • Value of A and B are not both 0 • Value of A, B, and C are real number constants • Ex) 3x + 2y = 6 • Subtract 3x from both sides of equation, 2y = –3x + 6 !!! • Then, divide both sides of equation by 2 for 𝑦 = ! + 3 • Lines can be graphed by identifying the transformations on the linear parent function, y = x !!! • Ex) 𝑦 = +3 ! • Reflected over the y-axis • Vertically stretched • Vertically translated up the y-axis by 3 • (0,3) is the y-intercept • Slope is –3/2 Slope-intercept form of a line • Advantages of slope-intercept form • Equation can be written quickly if slope and y-intercept are The slope-intercept form of an known equation of a line is in the form • Slope and y-intercept recognized immediately in equation y = mx + b where m is the slope of the line, and b and line can be graphed quickly is the y-intercept. [Page 1 of 2] Algebra II 2.4 Linear Equations Linear Equations Point-Slope Form Point-slope form of a line • When a slope is given without a y-intercept, an equation can be formed from a point on the line • Must apply transformations to the linear parent function • Ex) If slope is 1/2, then the graph should be vertically ! compressed, 𝑦 = ! 𝑥 • If the point on the line is (4,5), then translate to the right by ! four units and up by five units, 𝑦 = 𝑥 − 4 + 5 ! The point-slope form of the equation of a line is y – y1 = m(x – x1) where m is the slope of the line, and (x1,y1) is a point on the line. ! • Value of y can be moved to the other side, 𝑦 − 5 = ! (𝑥 − 4) • Advantages of point-slope form • Equation can be formed quickly from the slope and one point of a line • Can find y-intercept by solving the equation for y and converting the equation into slope-intercept form Horizontal & Vertical Lines • Sometimes linear equations do not appear to contain both x- and y-components • Ex) y = 4 • Two points on the line are (–3,4) and (5,4) ! !! !!! ! • Slope is !! !!! = !!(!!) = ! = 0 ! ! • Slope–intercept form is y = 0x + 4, point–slope equation is y – 4 = 0(x – 5) • Ex) x = 4 • Two points on the line are (4, –2) and (4,3) • Slope is !! !!! !! !!! = !!(!!) !!! ! = = undefined ! • Impossible to write equation of a vertical line in slope–intercept or point–slope form [Page 2 of 2] Algebra II 2.4 Linear Equations