5.1 Slope-Intercept Form OBJECTIVE 1 : Use slope-intercept form to write an equation of a line. Slope-Intercept Form: The slope-intercept form of the equation of a line with slope m and y-intercept b is y = mx + b

If you are given or can determine the slope and y-intercept of a line, you can write the equation in slope-intercept form. 2. Substitute the slope for m and the y-intercept for b. Steps to write equation in Slope-Intercept Form: EXAMPLE y = 3x + ( – 4) y = 3x – 4 Write the equation of the line whose slope is 3 and whose y-intercept is –4 1. Determine the slope and y-intercept. m = 3, b = –4

EXAMPLE Write the equation of a line with the slope of -4 and the y-intercept of 5. m = - 4 b = 5 y = mx + b y = - 4x + 5

EXAMPLE 2. y = mx + b 3. y = 5x + ( – 2) 4. y = 5x – 2 Write the equation of the line shown in the graph using slope-intercept form. 1. Use two points on the graph to determine slope. Use the graph to determine the y-intercept

EXAMPLE Write the equation of the line shown on the graph in slope-intercept form. y –intercept (0,3) Slope: m = = y = mx + b y = x +3 b = 3 Slope

OBJECTIVE 2: Model a real-life situation with a linear function. EXAMPLE The number of trout in a lake was estimated at 45 thousand in During the next 10 years, the trout population is expected to increase by about 3 thousand per year. 1. Identify the b ( the starting point) b = 45, Identify the m ( the rate of change) m = Write the equation in slope-intercept form. y = 3000x + 45,000

EXAMPLE A plumber charges $66 for the service call and $45 for each hour. Write the linear model to reflect the plumber’s charges. Use the equation to determine the cost of a 3 hour service call. 1. Identify b ( the starting point) b = Identify m (the rate of change) m = Write the equation. y = 45x Let x = 3 and substitute into the equation. y = 45(3) + 66 y = Y =201$201