ANote the important features of graph and then compare those requirements with the given equations.
BNote the important features of graph and then compare those requirements with the given equations.
CNote the important features of graph and then compare those requirements with the given equations.
DNote the important features of graph and then compare those requirements with the given equations.
Ay=1/3x+5
By=7/4x-1/4 and y=2x-4
Cy=-3x+8
Dy=-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.
