Question

equations in slope-intercept form
identify the slope and y-intercept of each line from an equation
(make sure each equation is in slope-intercept form).

1. ( y = 2x + 1 )

( m = ) ____ ( b = ) ____

1. ( y = \frac{1}{3}x - 2 )

( m = ) ____ ( b = ) ____

1. ( y = -\frac{2}{3}x + 1 )

( m = ) ____ ( b = ) ____

1. ( y + 2x = -3 )

( m = ) ____ ( b = ) ____

1. ( 4x - 6y = -12 )

( m = ) ____ ( b = ) ____

1. ( -x + \frac{1}{5}y = -3 )

( m = ) ____ ( b = ) ____
identify the slope and y-intercept of each line from a graph.
7.
graph of a line on a coordinate plane with points plotted
( m = ) ______
( b = ) ______
( x )-intercept = ______
8.
graph of a line on a coordinate plane with points plotted
( m = ) ______
( b = ) ______
( x )-intercept = ______
9.
graph of a horizontal line on a coordinate plane with points plotted
( m = ) ______
( b = ) ______
( x )-intercept = ______
10.
graph of a line on a coordinate plane with points plotted
( m = ) ______
( b = ) ______
( x )-intercept = ______

Explanation:

Step1: Recall slope-intercept form

Slope-intercept form is $y = mx + b$, where $m$ is slope and $b$ is y-intercept. For non-slope-intercept equations, rearrange to solve for $y$. For graphs, find $b$ (y-intercept, where $x=0$) and calculate $m = \frac{\Delta y}{\Delta x}$ using two points.

Step2: Solve equations 1-6

1. $y=2x+1$ → $m=2$, $b=1$
2. $y=\frac{1}{3}x-2$ → $m=\frac{1}{3}$, $b=-2$
3. $y=-\frac{2}{3}x+1$ → $m=-\frac{2}{3}$, $b=1$
4. $y=-2x-3$ → $m=-2$, $b=-3$
5. $y=\frac{2}{3}x+2$ → $m=\frac{2}{3}$, $b=2$
6. $y=5x-15$ → $m=5$, $b=-15$

Step3: Analyze graphs 7-10

1. Points: $(-4,6)$ & $(3,0)$ → $m=\frac{0-6}{3-(-4)}=-\frac{6}{7}$; y-intercept: ~$3.43$ (approx $\frac{24}{7}$); x-intercept: $3$
2. Points: $(0,-1)$ & $(3,2)$ → $m=\frac{2-(-1)}{3-0}=1$; y-intercept: $-1$; x-intercept: $1$
3. Horizontal line $y=2$ → $m=0$, $b=2$; no x-intercept (parallel to x-axis)
4. Points: $(-2,-1)$ & $(3,-3)$ → $m=\frac{-3-(-1)}{3-(-2)}=-\frac{2}{5}$; y-intercept: ~$-1.8$ (approx $-\frac{9}{5}$); x-intercept: ~$-4.5$ (approx $-\frac{9}{2}$)

Answer:

1. $m=2$, $b=1$
2. $m=\frac{1}{3}$, $b=-2$
3. $m=-\frac{2}{3}$, $b=1$
4. $m=-2$, $b=-3$
5. $m=\frac{2}{3}$, $b=2$
6. $m=5$, $b=-15$
7. $m=-\frac{6}{7}$, $b=\frac{24}{7}$, $x$-intercept=$3$
8. $m=1$, $b=-1$, $x$-intercept=$1$
9. $m=0$, $b=2$, $x$-intercept=none
10. $m=-\frac{2}{5}$, $b=-\frac{9}{5}$, $x$-intercept=$-\frac{9}{2}$