Question

on questions 1 - 9, graph each linear equation in the space provided.

1. $y = 3x + 1$

grid for graphing $y = 3x + 1$

1. $y = -5x - 4$

grid for graphing $y = -5x - 4$

Explanation:

For \( y = 3x + 1 \)

Step1: Identify the slope and y-intercept

The equation is in slope - intercept form \( y=mx + b \), where \( m \) is the slope and \( b \) is the y - intercept. For \( y = 3x+1 \), the slope \( m = 3=\frac{3}{1} \) and the y - intercept \( b = 1 \). So the line passes through the point \( (0,1) \) (since when \( x = 0 \), \( y=1 \)).

Step2: Use the slope to find another point

The slope \( \frac{3}{1} \) means that for every 1 unit we move to the right (increase in \( x \) by 1), we move up 3 units (increase in \( y \) by 3). Starting from \( (0,1) \), if we move \( x = 0+1 = 1 \), then \( y=1 + 3=4 \). So another point on the line is \( (1,4) \).

Step3: Plot the points and draw the line

Plot the points \( (0,1) \) and \( (1,4) \) on the given grid. Then draw a straight line passing through these two points.

For \( y=- 5x-4 \)

Step1: Identify the slope and y-intercept

The equation \( y=-5x - 4 \) is in slope - intercept form \( y = mx + b \), where \( m=-5=\frac{- 5}{1} \) and \( b=-4 \). So the line passes through the point \( (0,-4) \) (when \( x = 0 \), \( y=-4 \)).

Step2: Use the slope to find another point

The slope \( \frac{-5}{1} \) means that for every 1 unit we move to the right (increase \( x \) by 1), we move down 5 units (decrease \( y \) by 5). Starting from \( (0,-4) \), if \( x=0 + 1=1 \), then \( y=-4-5=-9 \). Another point on the line is \( (1,-9) \). We can also use a negative run (move left) and positive rise. If we move \( x = 0-1=-1 \), then \( y=-4+5 = 1 \), so the point \( (-1,1) \) is also on the line.

Step3: Plot the points and draw the line

Plot the points \( (0,-4) \) and \( (-1,1) \) (or \( (1,-9) \)) on the given grid. Then draw a straight line passing through these two points.

(Note: Since the problem is about graphing linear equations, the final answer is the graphical representation as described in the steps above. If we were to describe the key points for each line:
For \( y = 3x+1 \): Passes through \( (0,1) \) and \( (1,4) \)
For \( y=-5x - 4 \): Passes through \( (0,-4) \) and \( (-1,1) \))

Answer:

Step1: Identify the slope and y-intercept

The equation \( y=-5x - 4 \) is in slope - intercept form \( y = mx + b \), where \( m=-5=\frac{- 5}{1} \) and \( b=-4 \). So the line passes through the point \( (0,-4) \) (when \( x = 0 \), \( y=-4 \)).

Step2: Use the slope to find another point

The slope \( \frac{-5}{1} \) means that for every 1 unit we move to the right (increase \( x \) by 1), we move down 5 units (decrease \( y \) by 5). Starting from \( (0,-4) \), if \( x=0 + 1=1 \), then \( y=-4-5=-9 \). Another point on the line is \( (1,-9) \). We can also use a negative run (move left) and positive rise. If we move \( x = 0-1=-1 \), then \( y=-4+5 = 1 \), so the point \( (-1,1) \) is also on the line.

Step3: Plot the points and draw the line

Plot the points \( (0,-4) \) and \( (-1,1) \) (or \( (1,-9) \)) on the given grid. Then draw a straight line passing through these two points.

(Note: Since the problem is about graphing linear equations, the final answer is the graphical representation as described in the steps above. If we were to describe the key points for each line:
For \( y = 3x+1 \): Passes through \( (0,1) \) and \( (1,4) \)
For \( y=-5x - 4 \): Passes through \( (0,-4) \) and \( (-1,1) \))