Objective The student will be able to: write equations using slope-intercept form. identify slope and y-intercept from an equation.

Important!!! This is one of the big concepts in Algebra 1. You need to thoroughly understand this! Slope – Intercept Form y = mx + b m represents the slope b represents the y-intercept

Writing Equations When asked to write an equation, you need to know two things – slope (m) and y- intercept (b). There are two types of problems you will face.

Writing Equations – Type #1 Write an equation in slope-intercept form of the line that has a slope of 2 and a y-intercept of 6. To write an equation, you need two things: slope (m) = y – intercept (b) = We have both!! Plug them into slope-intercept form y = mx + b y = 2x + 6 2 6

Writing Equations – Type #2 Write an equation of the line that has a slope of 3 and goes through the point (2,1). To write an equation, you need two things: slope (m) = y – intercept (b) = We have to find the y-intercept!! Plug in the slope and ordered pair into y = mx + b 1 = 3(2) + b 3 ???

Writing Equations – Type #2 1 = 3(2) + b Solve the equation for b 1 = 6 + b -6 -6 -5 = b To write an equation, you need two things: slope (m) = y – intercept (b) = y = 3x - 5 3 -5

Find the slope and y-intercept. y = 3x – 7 y = mx + b m = 3, b = -7 To find the slope and y-intercept of an equation, write the equation in slope-intercept form: y = mx + b. Find the slope and y-intercept. y = 3x – 7 y = mx + b m = 3, b = -7

Find the slope and y-intercept. y = x y = mx + b y = x + 0 2) y = 5 y = 0x + 5 m = b = 0 m = 0 b = 5

Find the slope and y-intercept. 5x - 3y = 6 Write it in slope-intercept form. (y = mx + b) 5x – 3y = 6 -3y = -5x + 6 y = x - 2 -3 -3 -3 m = b = -2

Find the slope and y-intercept. 2y + 2 = 4x Write it in slope-intercept form. (y = mx + b) 2y + 2 = 4x 2y = 4x - 2 y = 2x - 1 m = 2 b = -1 2 2 2

Try These! Suppose we have a line with a slope of -1 and passes through the point (3, 4). Suppose we have a line with a slope of 2 and passes through the point (1, 3).

Write the Equation of a Line from a Graph Where does the line cross the y-axis? At the point (0, -4) The y-intercept is -4. What is the slope of the line? The graph also crosses the x-axis at (2, 0). We can use the slope formula to find our slope. m = -4 – 0 = -4 = 2 0 – 2 -2 We know our slope is 2 and our y-intercept is -4, what is the equation of our line? y = mx + b y = 2x + (-4) y = 2x -4

Using a graph Where does the line cross the y-axis? At the point (0, 2) So the y-intercept b is 2. The line also passes through the point (3, 0). We can use these points to find the slope of the line. How? What formula do we use? Using the slope formula, we find that the slope m is -2/3. Write the equation of the line. y= mx + b y = (-2/3)x + 2

Slope-Intercept Form– requires the y-intercept and the slope of the line.

Slope-Intercept Form:

Slope-Intercept Form:

 

Solving Problems The pool Entertainment company learned that by pricing a pool toy at $10, local sales will reach 200 a week. Lowering the price to $9 will cause sales to rise to 250 a week. a. Assume that the relationship between sales price and number of toys sold is linear. Write an equation that describes the relationship in slope-intercept form. Use ordered pairs of the form (sales price, number sold). b. Predict the weekly sales of the toy if the price is $7.50.

Solving Problems

Solving Problems Predict the weekly sales of the toy if the price is $7.50.