Equation #1 is Graph #4
Equation #2 is Graph #1
Equation #3 is Graph #2
Equation #4 is Graph #3
Answer:
1). Equation 1 - Option 4 on the top row
2). Equation 2 - Option 1 from the bottom row
3). Equation 3 - Option 2 from the top row
4). Equation 4 - Option 2 from the bottom row.
Step-by-step explanation:
1). First equation given in the question is [tex]y=5x+\frac{1}{5}[/tex]
This equation represents a line with slope 5 and y-intercept as [tex]\frac{1}{5}[/tex]
4th option on the top row represents a line in which y grows with the increase in value of x, slope 5 and y-intercept as 0.2.
2). Equation 2 is [tex]y=-\frac{1}{5}x+5[/tex]
Since this line passes through two points (0, 5) and (5, 6)
Therefore, slope of the line = [tex]\frac{5-6}{0-5}=-\frac{1}{5}[/tex]
The given line is represented by slope [tex]\frac{1}{5}[/tex] and y-intercept 5 which matches with 1st graph from the bottom row.
3). Equation 3 is y = -5x - [tex]\frac{1}{5}[/tex]
Since graph 2 on the top row shows the negative slope of 5 and y-intercept as [tex]-\frac{1}{5}[/tex]
Therefore, graph 2 from the top row will be the answer.
4). Equation 4 is [tex]y=-\frac{1}{5}x-5[/tex] showing slope [tex]-\frac{1}{5}[/tex] and y-intercept as -5.
This line passes through two points (0, -5) and (-5, -6) therefore,
Slope = [tex]\frac{-6+5}{0+5}=-\frac{1}{5}[/tex] and y-intercept as -5
Graph number 2 from the bottom row represents the equation of the line.
