Algebra 1 Bell Ringer Find the slope of the line that passes through the points. 1.(2, –1), (4, 0) 2.(–1, –3), (1, 5) 3. A landscape architect charges $75 for a consulting fee and $30 per hour. Write an equation that shows the cost C as a function of time t (in hours).

Chapter 5 Writing Linear Equations Prerequisite Skills Page 280: 1-9

5-1 Objective: Write Linear Equations in Slope-Intercept Form

Review of Lingo Y-intercept Slope Slope-Intercept Form

Slope Intercept Form y = mx + b m = slope b = y-intercept

Use Slope and Y-intercept to Write an Equation Just plug it in! Write an equation of the line with a slope of 3 and a y-intercept of 5. What would the graph look like?

EXAMPLE 1 Use slope and y-intercept to write an equation Write an equation of the line with a slope of –2 and a y -intercept of 5. y = mx + b Write slope-intercept form. y = –2x + 5 Substitute –2 for m and 5 for b.

Question What if you had to write an equation just by looking at the graph? How would you do it?

EXAMPLE 2 Standardized Test Practice Which equation represents the line shown ? The line crosses the y- axis at (0, 3). So, the y- intercept is 3. y = mx + b Write slope-intercept form. 2 y = – x Substitute – for m and 3 for b. 5 = = – The slope of the line is rise run –2–

GUIDED PRACTICE for Examples 1 and 2 1. Slope is 8; y- intercept is –7. Write an equation of the line with the given slope and y -intercept. y = 8x – 7 ANSWER

GUIDED PRACTICE for Examples 1 and 2 2. Slope is ; y intercept is – Write an equation of the line with the given slope and y -intercept. y = 3 4 x – 3 ANSWER

More Examples Page 286: 11, 12

Using Two Points If you know where the y-intercept is and any other point on the line, then you can write an equation of the line. How?

EXAMPLE 3 Write an equation of a line given two points Write an equation of the line shown.

Write an equation of a line given two points y = mx + b y = x – Substitute for m and  5 for b. 4 3 STEP 1 Write an equation of the line. The line crosses the y -axis at (0, –5). So, the y- intercept is –5. SOLUTION x 2 – x – 0 y 2 – y 1 = m = –1 – (–5) = 4 Write slope-intercept form. EXAMPLE 3 Calculate the slope. STEP 2

More Examples Guided Practice #3 on bottom of page 284 Page 287: 23

Function Notation Review of Function Notation Evaluate f(x) = 2x + 1 when x = 3 f(3) = 2(3) + 1 f(3) = 7 *This represents the point (3, 7)

Practice f(x) = 2x – 3 when x = 7, what point would this be? f(x) = ½x – 7 when x = -6, what point would this be?

Question If you only see f(0) = 5 what point is this and why is it so valuable?

Example Write an equation for the linear function f with the values f(0) = -2 and f(3) = -6

Example Write an equation for the linear function f with values f(0) = 4 and f(9) = 10.

SOLUTION Write a linear function Write an equation for the linear function f with the values f(0) = 5 and f(4) = 17. Calculate the slope of the line that passes through (0, 5) and (4, 17). Write f(0) = 5 as (0, 5) and f (4) = 17 as (4, 17). EXAMPLE 4 STEP 1 x 2 – x 1 4 – 0 y 2 – y 1 = m = 17 – 5 = 4 12 = 3 STEP 2

y = mx + b Write slope-intercept form. y = 3x + 5 Substitute 3 for m and 5 for b. Write an equation of the line. The line crosses the y -axis at (0, 5). So, the y- intercept is 5. STEP 3 EXAMPLE 4 Write a linear function ANSWER The function is f(x) = 3x + 5.

GUIDED PRACTICE for Examples 3 and 4 3. Write an equation of the line shown. 2 1 x + 1 y = ANSWER –

GUIDED PRACTICE for Examples 3 and 4 Write an equation for the linear function f with the given values f(0) = –2, f(8) = 4 y = x – ANSWER

GUIDED PRACTICE for Examples 3 and 4 Write an equation for the linear function f with the given values. 5. f(–3) = 6, f(0) = 5 y = x ANSWER –

Real-World Situations Remember key words: per, for each, for every…, etc., tells you to multiply. In this section, this will represent your slope.

Example The YMCA charges an initial membership fee of $45 and $60 per month to work out in the gym. Write an equation that gives the total cost of being a member and working out every month. Find the amount you would spend if you worked out every month for a year.

Look over Example 5

Homework 1, 2 – 36 ev, worksheet bonus 44, 52