Question

1. practice graph each line below.

a. $y = -\frac{3}{4}x - 4$
b. $-3x + 4y = 24$
c. $-3x - 4y = 16$
d. $-2y = 11$

Explanation:

Part a: Graph \( y = -\frac{3}{4}x - 4 \)

Step 1: Identify slope and y-intercept

The equation is in slope - intercept form \( y=mx + b \), where \( m =-\frac{3}{4} \) (slope) and \( b=- 4 \) (y - intercept). So the line crosses the y - axis at \( (0,-4) \).

Step 2: Use slope to find another point

The slope \( m =-\frac{3}{4}=\frac{\text{rise}}{\text{run}} \). From the y - intercept \( (0,-4) \), move down 3 units (because rise is - 3) and then 4 units to the right (run is 4) to get the point \( (4,-7) \). Or move up 3 units and 4 units to the left to get \( (-4,-1) \).

Step 3: Draw the line

Plot the points \( (0,-4) \), \( (4,-7) \), \( (-4,-1) \) and draw a straight line through them.

Part b: Graph \( - 3x+4y = 24 \)

Step 1: Find x - intercept (set \( y = 0 \))

Substitute \( y = 0 \) into the equation: \( -3x+4(0)=24\Rightarrow - 3x=24\Rightarrow x=-8 \). So the x - intercept is \( (-8,0) \).

Step 2: Find y - intercept (set \( x = 0 \))

Substitute \( x = 0 \) into the equation: \( -3(0)+4y=24\Rightarrow4y = 24\Rightarrow y = 6 \). So the y - intercept is \( (0,6) \).

Step 3: Draw the line

Plot the points \( (-8,0) \) and \( (0,6) \) and draw a straight line through them.

Part c: Graph \( -3x - 4y=36 \)

Step 1: Find x - intercept (set \( y = 0 \))

Substitute \( y = 0 \) into the equation: \( -3x-4(0)=36\Rightarrow - 3x=36\Rightarrow x=-12 \). So the x - intercept is \( (-12,0) \).

Step 2: Find y - intercept (set \( x = 0 \))

Substitute \( x = 0 \) into the equation: \( -3(0)-4y=36\Rightarrow - 4y=36\Rightarrow y=-9 \). So the y - intercept is \( (0,-9) \).

Step 3: Draw the line

Plot the points \( (-12,0) \) and \( (0,-9) \) and draw a straight line through them.

Part d: Graph \( -2y = 11 \)

Answer:

Step 1: Solve for y

Divide both sides of the equation \( -2y=11 \) by - 2: \( y=-\frac{11}{2}=-5.5 \).

Step 2: Identify the line type

This is a horizontal line because for all values of \( x \), \( y=-5.5 \). So we can plot points like \( (0,-5.5) \), \( (2,-5.5) \), \( (-2,-5.5) \) and draw a horizontal line through them.

(Note: Since the question is about graphing lines, the above steps describe how to find the key points to plot the lines. If you need a more detailed graphical representation, you can use graphing paper and plot the points as described.)