Question

1. graph $y = -4x + 3$

1. graph the following using the slope and y-intercept. show all your calculations work.

$3x + 4y = 12$

Explanation:

Problem 8: Graph \( y = -4x + 3 \)

Step 1: Identify slope and y - intercept

The equation \( y=-4x + 3 \) is in slope - intercept form \( y=mx + b \), where \( m \) is the slope and \( b \) is the y - intercept. Here, \( m=-4 \) and \( b = 3 \).

Step 2: Plot the y - intercept

The y - intercept \( b = 3 \) means the line crosses the y - axis at the point \( (0,3) \). Plot this point on the coordinate plane.

Step 3: Use the slope to find another point

The slope \( m=-4=\frac{-4}{1} \). From the point \( (0,3) \), move down 4 units (because the numerator of the slope is - 4, which represents a change in \( y \)) and then move 1 unit to the right (because the denominator of the slope is 1, which represents a change in \( x \)). This gives the point \( (1,3 - 4)=(1,-1) \). Alternatively, you can move up 4 units and left 1 unit (since \( \frac{-4}{1}=\frac{4}{-1} \)) from \( (0,3) \) to get the point \( (-1,3 + 4)=(-1,7) \).

Step 4: Draw the line

Draw a straight line through the points \( (0,3) \) and \( (1,-1) \) (or the other point you found).

Problem 9: Graph \( 3x + 4y=12 \) using slope and y - intercept

Step 1: Convert to slope - intercept form

We need to solve the equation \( 3x + 4y = 12 \) for \( y \).
Subtract \( 3x \) from both sides: \( 4y=-3x + 12 \).
Divide each term by 4: \( y=\frac{-3x + 12}{4}=\frac{-3}{4}x+3 \).

Step 2: Identify slope and y - intercept

In the slope - intercept form \( y = mx + b \), \( m=-\frac{3}{4} \) (slope) and \( b = 3 \) (y - intercept).

Step 3: Plot the y - intercept

The y - intercept \( b = 3 \), so the line crosses the y - axis at \( (0,3) \). Plot this point.

Step 4: Use the slope to find another point

The slope \( m =-\frac{3}{4}=\frac{-3}{4} \). From the point \( (0,3) \), move down 3 units (change in \( y=-3 \)) and then move 4 units to the right (change in \( x = 4 \)) to get the point \( (4,3-3)=(4,0) \). Or, move up 3 units and left 4 units (since \( \frac{-3}{4}=\frac{3}{-4} \)) from \( (0,3) \) to get the point \( (-4,3 + 3)=(-4,6) \).

Step 5: Draw the line

Draw a straight line through the points \( (0,3) \) and \( (4,0) \) (or the other point you found).

Answer:

s:

• For \( y=-4x + 3 \): The line has a y - intercept at \( (0,3) \) and a slope of - 4. The graph is a straight line passing through \( (0,3) \) and \( (1,-1) \) (or other points found using the slope).
• For \( 3x + 4y = 12 \) (or \( y=-\frac{3}{4}x + 3 \)): The line has a y - intercept at \( (0,3) \) and a slope of \( -\frac{3}{4} \). The graph is a straight line passing through \( (0,3) \) and \( (4,0) \) (or other points found using the slope).