Note the important features of graph and then compare those requirements with the given equations.
B
Note the important features of graph and then compare those requirements with the given equations.
C
Note the important features of graph and then compare those requirements with the given equations.
D
Note the important features of graph and then compare those requirements with the given equations.
A
y=1/3x+5
B
y=7/4x-1/4 and y=2x-4
C
y=-3x+8
D
y=-4x-9 and y=- x-4/3
Practice makes perfect
We will note the important features of each graph and then compare those requirements to the given equations. Let's look at graph A.
As we can see, A has a positive slope as it is slanting upwards. Also, the graph intercepts the y-axis at a positive value. Therefore, the y-intercept is a positive number. Let's look at each of the given equations to see which one satisfies these conditions.
Function
Slope
y-intercept
y= -3x + 8
Negative
Positive
y=-7x ⇕ y= - 7x + 0
Negative
0
y= 7/4x - 1/4
Positive
Negative
y= -4x - 9
Negative
Negative
y=- x-4/3 ⇕ y= - 1x - 4/3
Negative
Negative
y= 2x - 4
Positive
Negative
y= 1/3x + 5
Positive
Positive
y=6 ⇕ y= 0x + 6
0
Positive
We can see that the equation y = 13x + 5 has positive slope and y-intercept. Therefore, we can use graph A to represent that equation.
Let's look at graph B.
As we can see, B has a positive slope and a negative y-intercept. Let's look at each of the given equations to see which one satisfies these.
Function
Slope
y-intercept
y= -3x + 8
Negative
Positive
y= - 7x + 0
Negative
0
y= 7/4x - 1/4
Positive
Negative
y= -4x - 9
Negative
Negative
y= - 1x - 4/3
Negative
Negative
y= 2x - 4
Positive
Negative
y= 1/3x + 5
Positive
Positive
y= 0x + 6
0
Positive
We can see that equations y= 74x- 14 and y=2x-4 both have a positive slope and a negative y-intercept. Therefore, we can use graph B to represent those equations.
Let's look at graph C.
The graph is slanting downwards, which means it has a negative slope. Also, since the graph intercepts the y-axis above the x-axis, its y-intercept is positive. Let's look at each of the given equations to see which one satisfies these.
Function
Slope
y-intercept
y= -3x + 8
Negative
Positive
y= - 7x + 0
Negative
0
y= 7/4x - 1/4
Positive
Negative
y= -4x - 9
Negative
Negative
y= - 1x - 4/3
Negative
Negative
y= 2x - 4
Positive
Negative
y= 1/3x + 5
Positive
Positive
y= 0x + 6
0
Positive
We can see that the equation y=-3x + 8 has a negative slope and a positive y-intercept. Therefore, we can use graph C to represent that equation.
Finally, let's look at graph D.
Here, the graph is slanting downwards and therefore it has a negative slope. Also, since the graph intercepts the y-axis below the x-axis, its y-intercept is negative. Let's look at each of the given equations to see which one satisfies these.
Function
Slope
y-intercept
y= -3x + 8
Negative
Positive
y= - 7x + 0
Negative
0
y= 7/4x - 1/4
Positive
Negative
y= -4x - 9
Negative
Negative
y= - 1x - 4/3
Negative
Negative
y= 2x - 4
Positive
Negative
y= 1/3x + 5
Positive
Positive
y= 0x + 6
0
Positive
We can see that equations y=-4x-9 and y=- x- 43 both have a negative slope and a negative y-intercept. Therefore, we can use graph D to represent those equations.
