Question

6.1 slope intercept form
after this section you should be able to:

• identify the slope and y-intercept of a straight line graph
• determine a linear equation using the slope and y-intercept
• rewrite a linear equation in slope intercept form
• graph equations in slope-intercept form
• solve problems using equations in slope intercept form
• the y-intercept is the y-coordinate of the point where a line crosses the y-axis i.e. it has the coordinates (0, y)
• the slope-intercept form is a linear equation written in the form $y = mx + b$ where $m$ is the slope and $b$ is the y-intercept

ex. 1 find the slope and y-intercept of the following.

1. $y = \frac{1}{3}x + 2$
2. $y = -4x - 1$

ex. 2 find the slope and y-intercept of the following. hint: rearrange the equation into slope-intercept form first.

1. $4x + 3y = 9$
2. $2x - 4y = -8$

Explanation:

Ex. 1, Problem 1: Match to slope-intercept form

The slope-intercept form is $y=mx+b$, where $m$ is slope, $b$ is y-intercept.
For $y=\frac{1}{3}x+2$, compare directly:
$m=\frac{1}{3}$, $b=2$

Ex. 1, Problem 2: Match to slope-intercept form

For $y=-4x-1$, compare directly to $y=mx+b$:
$m=-4$, $b=-1$

Ex. 2, Problem 1: Isolate $y$ to rewrite form

Step1: Subtract $4x$ from both sides
$4x+3y-4x=9-4x \implies 3y=-4x+9$
Step2: Divide all terms by 3
$\frac{3y}{3}=\frac{-4x}{3}+\frac{9}{3} \implies y=-\frac{4}{3}x+3$
Step3: Identify $m$ and $b$
$m=-\frac{4}{3}$, $b=3$

Ex. 2, Problem 2: Isolate $y$ to rewrite form

Step1: Subtract $2x$ from both sides
$2x-4y-2x=-8-2x \implies -4y=-2x-8$
Step2: Divide all terms by $-4$
$\frac{-4y}{-4}=\frac{-2x}{-4}+\frac{-8}{-4} \implies y=\frac{1}{2}x+2$
Step3: Identify $m$ and $b$
$m=\frac{1}{2}$, $b=2$

Answer:

Ex. 1

1. Slope: $\frac{1}{3}$, Y-intercept: $2$
2. Slope: $-4$, Y-intercept: $-1$

Ex. 2

1. Slope: $-\frac{4}{3}$, Y-intercept: $3$
2. Slope: $\frac{1}{2}$, Y-intercept: $2$