Question

1. $y + 5 = \frac{1}{4}(x - 2)$
2. $y = -(x + 4)$
3. $y + 1 = -\frac{2}{3}(x + 1)$
4. $y + 2 = 3x$

Explanation:

Problem 15: \( y + 5 = \frac{1}{4}(x - 2) \)

Step 1: Identify the form

The equation \( y + 5 = \frac{1}{4}(x - 2) \) is in point - slope form \( y - y_1=m(x - x_1) \), where \( (x_1,y_1)=(2,-5) \) and the slope \( m = \frac{1}{4} \).

Step 2: Plot the point

First, plot the point \( (2,-5) \) on the coordinate plane.

Step 3: Use the slope

The slope \( m=\frac{1}{4}=\frac{\text{rise}}{\text{run}} \). From the point \( (2,-5) \), move up 1 unit (since rise is 1) and then move to the right 4 units (since run is 4) to get another point \( (2 + 4,-5+1)=(6,-4) \).

Step 4: Draw the line

Draw a straight line passing through the points \( (2,-5) \) and \( (6,-4) \).

Problem 16: \( y=-(x + 4) \)

Step 1: Rewrite in slope - intercept form

Rewrite \( y=-(x + 4) \) as \( y=-x - 4 \). The slope - intercept form is \( y=mx + b \), where the slope \( m=-1 \) and the y - intercept \( b=-4 \).

Step 2: Plot the y - intercept

Plot the point \( (0,-4) \) (since the y - intercept is at \( x = 0,y=-4 \)) on the coordinate plane.

Step 3: Use the slope

The slope \( m=-1=\frac{- 1}{1}=\frac{\text{rise}}{\text{run}} \). From the point \( (0,-4) \), move down 1 unit (since rise is - 1) and then move to the right 1 unit (since run is 1) to get the point \( (0 + 1,-4-1)=(1,-5) \), or move up 1 unit and move to the left 1 unit to get \( (0-1,-4 + 1)=(-1,-3) \).

Step 4: Draw the line

Draw a straight line passing through the points \( (0,-4) \) and \( (1,-5) \) (or \( (0,-4) \) and \( (-1,-3) \)).

Problem 17: \( y + 1=-\frac{2}{3}(x + 1) \)

Step 1: Identify the form

The equation \( y + 1=-\frac{2}{3}(x + 1) \) is in point - slope form \( y - y_1=m(x - x_1) \), where \( (x_1,y_1)=(-1,-1) \) and the slope \( m=-\frac{2}{3} \).

Step 2: Plot the point

Plot the point \( (-1,-1) \) on the coordinate plane.

Step 3: Use the slope

The slope \( m =-\frac{2}{3}=\frac{\text{rise}}{\text{run}} \). From the point \( (-1,-1) \), move down 2 units (since rise is - 2) and then move to the right 3 units (since run is 3) to get the point \( (-1+3,-1 - 2)=(2,-3) \), or move up 2 units and move to the left 3 units to get \( (-1-3,-1 + 2)=(-4,1) \).

Step 4: Draw the line

Draw a straight line passing through the points \( (-1,-1) \) and \( (2,-3) \) (or \( (-1,-1) \) and \( (-4,1) \)).

Problem 18: \( y + 2=3x \)

Answer:

Step 1: Rewrite in slope - intercept form

Rewrite \( y + 2=3x \) as \( y=3x-2 \). The slope - intercept form is \( y = mx + b \), where the slope \( m = 3 \) and the y - intercept \( b=-2 \).

Step 2: Plot the y - intercept

Plot the point \( (0,-2) \) (since when \( x = 0,y=-2 \)) on the coordinate plane.

Step 3: Use the slope

The slope \( m = 3=\frac{3}{1}=\frac{\text{rise}}{\text{run}} \). From the point \( (0,-2) \), move up 3 units (since rise is 3) and then move to the right 1 unit (since run is 1) to get the point \( (0 + 1,-2+3)=(1,1) \).

Step 4: Draw the line

Draw a straight line passing through the points \( (0,-2) \) and \( (1,1) \).