Graphing Linear Equations

Which of the following represents a graph of a linear equation?

• 
• 
• 
• 

The point where the line crosses the y-axis is called the:

• origin

• x-intercept

• y-intercept

• slope

Answer explanation

The y-intercept is the point where a line or function intercepts, or crosses, the y-axis. In a coordinate system, this point is where the x-coordinate is 0. Hence, in the given question, the point where the line crosses the y-axis is correctly referred to as the y-intercept.

Give the equation for the graph

• y = 5x - 3

• y = 4x + 2

• y =-2x + 5

• y = - 2x + 4

Answer explanation

The question asks for the equation of the graph. The correct answer is 'y = - 2x + 4'. This equation defines a line in a two-dimensional space. Its slope is -2, and it crosses the y-axis at 4. Other options may represent valid equations for some graphs, but they do not match the required equation in this specific case.

^{What is the x- intercept of the line?}

• x = 1

• x = 2

• x = -1

• x = -2

Answer explanation

The x-intercept of a line is the point at which it crosses the x-axis. Since the x-axis is defined as y=0, the x-intercept is the value of x when y=0. In this case, the line crosses the x-axis at x = -1. Therefore, the correct answer to the question is 'x = -1'.

The letter that represents the slope in the equation y = mx + b is _____.

Answer explanation

In the linear equation y = mx + b, 'm' represents the slope. It's the coefficient of 'x', which means it determines the rate of change of 'y' with respect to 'x'. Therefore, 'm' is the correct answer to the question about which letter represents the slope in the given equation.

Tags

CCSS.8.EE.B.6

CCSS.8.F.A.3

What is the y-intercept for the following equation where (1,4) is a solution, y = -3x + _____

Answer explanation

The equation y = -3x + 7 is in the slope-intercept form, where the y-intercept is the constant term. In this case, the y-intercept is 7, which is the correct option.

Tags

CCSS.8.EE.B.6

CCSS.8.F.A.3

Which quadrant is (9, 2) located?

• I

• II

• III

• IV

Answer explanation

The question asks in which quadrant the point (9, 2) is located. The point (9, 2) is in the first quadrant or 'I', as both coordinates are positive. In the Cartesian coordinate system, the first quadrant comprises all points with positive x and y coordinates.

Tags

CCSS.6.NS.C.6B

Which is the graph of y= -x + 2?

• A

• B

• C

• D

Answer explanation

The graph of the equation y = -x + 2 is a straight line with a slope of -1 and y-intercept of 2. Option 'A' correctly represents this graph. The line starts at point (0,2) on the y-axis and slopes downwards, indicating a negative slope, which matches the equation.

_{The y-intercept of the line is _____.}

Answer explanation

The y-intercept of a line is its value at x=0. It is the point where the line crosses the y-axis. In the given options, 'y = -1' is the correct choice. This means that the line crosses the y-axis at -1. Thus, the y-intercept of the line is -1.

Identify the y-intercept for the function:
y=-3x

• -3

• 0

• 1

• -1

Answer explanation

The y-intercept of a linear function is the value of 'y' when 'x' is 0. In the given function, y = -3x, by substituting x = 0, we get y = 0. Therefore, '0' is the correct answer, which is the y-intercept of the function.