IB Math Studies Yr 1

Name_________________________________ Date_______________

4-2 Gradient-Intercept Form of a Line

Today’s Learning Goals:

#3: What is the gradient-intercept form of a line? How do we write the equation of a line in gradient-intercept form?

Warm Up:

1. P(-7, 8) and Q(5, 12) are points on the coordinate plane. Determine the gradient of the line drawn through

P and Q.

2. Find the gradient of the line in the following graph.

Gradient-Intercept Form of a Linear Equation

The gradient-intercept form is probably the most frequently used way to express the equation of a line.

In general, the gradient-intercept form assumes the formula: 𝒚 = 𝒎𝒙 + 𝒄

In this form, it is very easy to identify the gradient and y-intercept of the line.

𝒎 is the ______________ of the line

𝒄 is the __________________ of the line

IB Math Studies Yr 1

What if we have the equation of a line? In order to correctly identify the gradient and y-intercept of a line, first make sure the line is expressed

in gradient-intercept form (𝒚 = 𝒎𝒙 + 𝒄).

DIRECTIONS: Determine the gradient and y-intercept of the equations below.

a. 𝑦 = −2𝑥 − 4

b. 𝑦 = −3

4𝑥

c. 𝑦 =𝑥

2+ 4 d. 𝑦 = 5

e. 4𝑦 = 8𝑥 + 4

f. 3𝑥 + 𝑦 = 12

g. 𝑦 − 3 =5𝑥

2 h. 10𝑥 − 5𝑦 = 25

i. 2𝑥 + 4𝑦 + 6 = 0 j. −3𝑥 + 5𝑦 − 16 = 0

IB Math Studies Yr 1

WRITING THE EQUATION OF A LINE GIVEN A GRAPH IN SLOPE-INTERCEPT FORM:

You Try:

1. Identify the gradient and y-intercept of the graphs below. Then write the equation of the lines in gradient-

intercept form.

Steps as we Go! Guided Example: Determine the equation for the following graphed line

Before we start, we know for any linear equation, we need a slope, and a y-intercept! We will solve for slope 1st

Part I. Determining the slope

1. Pick 2 clean points

2. Select the left most point. Count how many units vertically it takes so it’s on the same level as the 2nd point. Then count how many units horizontally it takes to get to the 2nd point

3. Plug in: 𝒎 =𝒓𝒊𝒔𝒆

𝒓𝒖𝒏=

𝟏

𝟐

Part II. Writing the equation:

1. Make sure you have the slope (m) 2. Find the y-intercept (where does the

line cross the y-axis?) (b) 3. Plug into y = mx + b!

𝒚 = 𝒎𝒙 + 𝒄

𝒎 =𝟏

𝟐 𝒄 = 𝟑

𝒚 =𝟏

𝟐𝒙 + 𝟑

IB Math Studies Yr 1

Let’s Try It! 1. For each of the following graphs identify the gradient and y-intercept. Then write the equation of each line in

gradient-intercept form.

Equations of Special Lines: Horizontal Lines Horizontal lines only travel through the y-axis, no x-intercept here! Example Equation: y = -1 Slope =

Vertical Lines Here, because the line doesn’t travel through the y-axis, we need an x-intercept. Example Equation: x = -2 Slope:

The slope for all horizontal lines is _________________

The slope for all vertical lines is _________________

IB Math Studies Yr 1

2. Determine the gradient and y-intercept of the equations below. Careful! - You might need to solve for

gradient-intercept form first.

a. 𝑦 =4

5𝑥 + 2

b. 𝑦 = −𝑥

c. 𝑦 =𝑥

3−

1

2 d. 3𝑦 = −9𝑥 + 6

e. 𝑦 + 6 = 𝑥

f. 4𝑥 − 𝑦 = 7

g. 2𝑥 + 3𝑦 − 5 = 0 h. 𝑥 +1

2𝑦 − 3 = 0

3. Determine the slope of the line connecting the points (-3, 4) and (5, -3) using the gradient formula

IB Math Studies Yr 1

Name: _____________________________________________

Date: ______________________________________________

4-2 Homework

1. Write the equation of the linear function depicted in the graph below.

a.

2. Write the following in slope intercept form:

a. 𝑦 + 5 =1

3(𝑥 − 1)

b. −6𝑥 – 2𝑦 = −2

c. −𝑦 − 4𝑥 = 5

d. -2y – 3x = 2

Slope = _____________

y - Intercept = _____________

Equation:

______________________________

IB Math Studies Yr 1

3. Calculate the midpoint, length, and gradient of the line segment with endpoints of: A(-3, 8) and B(7, 2)

Gradient Midpoint Length

4. Write the equation of the line below in gradient-intercept form:

5. What is the equation of the line below: