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

Slope-intercept form is $y=mx+b$. For $y=\frac{1}{3}x+2$, $m=\frac{1}{3}$, $b=2$.

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

For $y=-4x-1$, $m=-4$, $b=-1$.

Ex. 2, Problem 1: Isolate $y$

Start with $4x+3y=9$. Subtract $4x$:
$3y = -4x + 9$
Divide by 3:
$y = -\frac{4}{3}x + 3$
Now identify $m=-\frac{4}{3}$, $b=3$.

Ex. 2, Problem 2: Isolate $y$

Start with $2x-4y=-8$. Subtract $2x$:
$-4y = -2x - 8$
Divide by $-4$:
$y = \frac{1}{2}x + 2$
Now identify $m=\frac{1}{2}$, $b=2$.

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: $2$