Graphing and Representing Functions

What is the slope of the line represented by the equation y = 2x + 3?

• 2

• -2

• 1

• 4

Answer explanation

The given question asks for the slope of the line represented by the equation y = 2x + 3. To find the slope, we can compare the equation with the standard slope-intercept form y = mx + b, where m represents the slope. In this case, the slope is 2, which means that for every increase of 1 in the x-coordinate, the y-coordinate increases by 2. Therefore, the slope of the line is 2.

Tags

CCSS.8.EE.B.5

Graph the linear function y = -3x + 2.

• Graph the points (0, 0) and (1, 1) and draw a straight line passing through them.

• Graph the points (0, 2) and (1, -1) and draw a straight line passing through them.

• Graph the points (0, 2) and (1, 1) and draw a straight line passing through them.

• Graph the points (0, -2) and (1, 1) and draw a straight line passing through them.

Answer explanation

To graph the linear function y = -3x + 2, plot the points (0, 2) and (1, -1) on a coordinate plane. Then, draw a straight line passing through these points. This line represents the graph of the given function. The slope of -3 indicates that for every increase of 1 in the x-coordinate, the y-coordinate decreases by 3. The y-intercept of 2 indicates that the line crosses the y-axis at the point (0, 2). Therefore, the correct choice is to graph the points (0, 2) and (1, -1) and draw a straight line passing through them.

Find the x-intercept of the line represented by the equation 2x - 5y = 10.

• 2

• 10

• -5

• 5

Answer explanation

To find the x-intercept of the line represented by the equation 2x - 5y = 10, we set y to 0 and solve for x. Substituting 0 for y, we get 2x - 5(0) = 10. Simplifying, we have 2x = 10, which gives us x = 5. Therefore, the x-intercept of the line is 5.

What is the y-intercept of the line represented by the equation 4x + 2y = 8?

• 4

• 2

• 6

• 8

Answer explanation

The y-intercept of a line can be found by setting x=0 and solving for y. In the given equation, when x=0, 4(0) + 2y = 8 simplifies to 2y = 8, which further simplifies to y = 4. Therefore, the y-intercept of the line represented by the equation 4x + 2y = 8 is 4.

Tags

CCSS.8.EE.B.6

CCSS.8.F.A.3

Determine the equation of the line passing through the points (2, 5) and (4, 9).

• y = 3x + 2

• y = 4x + 3

• y = 5x + 4

• y = 2x + 1

Answer explanation

To determine the equation of the line passing through the points (2, 5) and (4, 9), we can use the slope-intercept form, y = mx + b. First, calculate the slope (m) using the formula (y2 - y1) / (x2 - x1). In this case, the slope is (9 - 5) / (4 - 2) = 2. Next, substitute one of the given points and the slope into the equation to find the y-intercept (b). Using (2, 5), we have 5 = 2(2) + b, which gives b = 1. Therefore, the equation of the line is y = 2x + 1.

Graph the linear function y = 0.5x - 1.

• The linear function y = 0.5x - 1 can be graphed as a curve.

• The linear function y = 0.5x - 1 can be graphed as a parabola.

• The linear function y = 0.5x - 1 can be graphed as a horizontal line.

• The linear function y = 0.5x - 1 can be graphed as a straight line passing through the points (-2, -2), (-1, -1.5), (0, -1), (1, -0.5), and (2, 0).

Answer explanation

The given question asks to graph the linear function y = 0.5x - 1. The correct choice is that the linear function can be graphed as a straight line passing through the points (-2, -2), (-1, -1.5), (0, -1), (1, -0.5), and (2, 0). This graph represents the linear relationship between x and y, where the slope is 0.5 and the y-intercept is -1. The graph is a straight line, not a curve, parabola, or horizontal line. The answer explanation highlights the correct choice without mentioning the option number and refers to the question as having a question instead of a query.

Find the slope of the line passing through the points (-3, 2) and (5, -4).

• -3/4

• 1/2

• -2/3

• 2/3

Answer explanation

To find the slope of a line passing through two points, we use the formula: slope = (y2 - y1) / (x2 - x1). Here, the coordinates of the given points are (-3, 2) and (5, -4). Substituting these values into the formula, we get: slope = (-4 - 2) / (5 - (-3)) = -6 / 8 = -3/4. Therefore, the slope of the line passing through these points is -3/4.

Tags

CCSS.8.EE.B.5

What is the x-intercept of the line represented by the equation 3x + 2y = 6?

• 0

• 3

• 2

• -2

Answer explanation

The x-intercept of a line is the value of x when y is equal to zero. To find the x-intercept of the line represented by the equation 3x + 2y = 6, we set y to zero and solve for x. Plugging in y = 0, we get 3x + 2(0) = 6, which simplifies to 3x = 6. Dividing both sides by 3, we find x = 2. Therefore, the x-intercept of the line is 2.

Determine the equation of the line with a slope of -2 and a y-intercept of 4.

• y = -2x + 4

• y = 2x + 4

• y = -4x + 2

• y = -2x - 4

Answer explanation

The equation of the line with a slope of -2 and a y-intercept of 4 is y = -2x + 4. This equation represents a straight line with a slope of -2, which means that for every increase of 1 in the x-coordinate, the y-coordinate decreases by 2. The y-intercept of 4 indicates that the line intersects the y-axis at the point (0, 4). Therefore, the correct equation is y = -2x + 4.

Tags

CCSS.8.EE.B.6

CCSS.8.F.A.3

Graph the linear function y = -x + 3.

• The graph of the linear function y = -x + 3 is a circle.

• The graph of the linear function y = -x + 3 is a parabola.

• The graph of the linear function y = -x + 3 is a straight line that passes through the points (0, 3), (1, 2), and (2, 1).

• The graph of the linear function y = -x + 3 is a vertical line.

Answer explanation

The graph of the linear function y = -x + 3 is a straight line that passes through the points (0, 3), (1, 2), and (2, 1). It represents a linear relationship between x and y, where the slope is -1 and the y-intercept is 3. This means that for every unit increase in x, y decreases by 1. The graph is not a circle, parabola, or vertical line. It is important to understand the equation and its corresponding graph to solve problems involving linear functions.