Question

state the slope and the y - intercept for the graph of each equation.

1. $y = 3x + 4$
2. $y = -\frac{3}{4}x - \frac{1}{4}$
3. $3x + y = - 6$

write an equation of a line in slope - intercept form with the given slope and y - intercept.

1. slope $-\frac{3}{4}$, y - intercept $- 2$
2. slope $\frac{2}{5}$, y - intercept $8$

Explanation:

Problem 1: \( y = 3x + 4 \)

Step1: Recall slope - intercept form

The slope - intercept form of a linear equation is \( y=mx + b \), where \( m \) is the slope and \( b \) is the \( y \)-intercept.

Step2: Identify \( m \) and \( b \)

For the equation \( y = 3x+4 \), comparing with \( y = mx + b \), we have \( m = 3 \) (slope) and \( b = 4 \) ( \( y \)-intercept).

Step1: Recall slope - intercept form

The slope - intercept form of a linear equation is \( y = mx + b \), where \( m \) is the slope and \( b \) is the \( y \)-intercept.

Step2: Identify \( m \) and \( b \)

For the equation \( y=-\frac{3}{4}x-\frac{1}{2} \), comparing with \( y = mx + b \), we have \( m=-\frac{3}{4} \) (slope) and \( b =-\frac{1}{2} \) ( \( y \)-intercept).

Step1: Rewrite in slope - intercept form

We need to solve the equation \( 3x + y=-6 \) for \( y \). Subtract \( 3x \) from both sides: \( y=-3x - 6 \).

Step2: Identify \( m \) and \( b \)

Now that the equation is in the form \( y = mx + b \) (where \( y=-3x - 6 \)), we can see that \( m=-3 \) (slope) and \( b=-6 \) ( \( y \)-intercept).

Answer:

Slope: \( 3 \), \( y \)-intercept: \( 4 \)

Problem 2: \( y=-\frac{3}{4}x-\frac{1}{2} \)