2.1 Slope-Intercept Form

2.1 Slope-Intercept Form

You will be able to write linear equations in slope-intercept form and interpret the slope and the intercept of a linear model.

Slope-Intercept Form

• m represents the slope

•  $m=slope=\frac{rise}{run}=\frac{y_2-y_1}{x_2-x_1}$  

• b represents the y-intercept

• the y-intercept is where the graph meets the y-axis

Multiple Choice

What does "m" represent in y=mx+b?

• y-intercept
• slope
• macaroni
• nothing

Multiple Choice

True or False: The y - intercept of a linear equation is where the line meets the x - axis.

• True

• False

Multiple Choice

The slope of a linear equation informs one how to get from

one point to the next.

• True

• False

Multiple Choice

What is the equation of a line with a slope of 2 and a y-intercept of -5?

• y = 5x - 2

• y = 2x - 5

• y = -2x - 5

• y = 2x + 5

Multiple Select

Select the slope AND the y - intercept from the following:

 $y=-\frac{2}{7}x+\frac{1}{9}$ 

•  $y-intercept=b=\frac{1}{9}$  

•  $y-intercept=b=-\frac{2}{7}$  

•  $slope=m=\frac{1}{9}$  

•  $slope=m=-\frac{2}{7}$  

Multiple Choice

What is the slope of the line with the equation
 $y\ =\ -\frac{3}{2}x\ +\ 4$  

•  $-4$  

•  $\frac{3}{2}$  

•  $4$  

•  $-\frac{3}{2}$  

EXAMPLE 1: Graph a Linear Equations

What is the graph of

 $y=\frac{4}{5}x+2$  ?

Multiple Choice

Which is the graph of

 $y=-\frac{5}{2}x+1$  ?

Finding the slope and y-intercept when you are given 2 points on the line:

• Find the slope (m)

• Use the slope (m) from part 1 and the formula: y = mx + b, to find the intercept (b)

Find the Slope Between 2 Points

• Find the slope using the slope formula

•  $m=\frac{y_2-y_1}{x_2-x_1}$  

Multiple Choice

Find the slope of the line.

• $-\frac{5}{7}$

• $\frac{7}{5}$

• $-\frac{7}{5}$

• $\frac{5}{7}$

Multiple Choice

Find the slope of the line that passes through the following:

 $\left(10,6\right)\ and\ \left(5,5\right)$  

•  $\frac{1}{5}$  

•  $-\frac{1}{5}$  

•  $5$  

•  $-5$  

Find the Y-Intercept

• Use the slope from the 1st step to plug in for m, in y = mx + b

• Use one of your points (x,y), it doesn't matter which one, to replace the x and y in the equation

• Solve for b

Write the Equation

Now using your slope (m) and y-intercept (b), write your equation into slope-intercept form.

The only variables you have should be the x and the y.

Multiple Choice

What is the equation of the line that passes through (1, 4) and (2, 1)

• y = -3x + 1

• y = -3x + 4

• y = -3x - 7

• y = -3x + 7

Multiple Choice

What is the equation of the line that passes through (-2, 3) and has a slope of 4?

• y = -2x + 3

• y = 4x - 2

• y = 4x + 3

• y = 4x + 11

Write an Equation from a Graph

• Choose 2 points on the line (HINT: use the y-intercept, if you can)

• Use the same process to find the slope and the y-intercept.

• If you can see the y-intercept easily, then you do not have to solve for b.

Multiple Choice

Write the equation for the line.

• $y=-1x+3$

• $y=4x+3$

• $y=\frac{1}{4}x+3$

• $y=-4x+3$

Open Ended

Jordan will hike the trail shown at a rate of 5 ​mi/h. Write a linear equation to represent the distance Jordan still has to walk after x hours. What does the​ y-intercept of the equation​ represent?

Multiple Choice

What does the​ y-intercept of the equation​ represent?

• The time the hike will take to complete

• The time at which Jordan starts to hike

• The rate at which Jordan hikes the trail

• The total length of the trail