Graphing Linear Equations

What is the slope-intercept form of a linear equation?

• y = ax + b

• y = mx - b

• y = mx^2 + b

• y = mx + b

Answer explanation

The slope-intercept form of a linear equation is given by y = mx + b, where m represents the slope and b represents the y-intercept. This equation is used to graph a linear equation on a coordinate plane. The correct choice is y = mx + b, which satisfies the conditions of the given question. The equation y = ax + b, y = mx - b, and y = mx^2 + b are incorrect choices. The question asks for the slope-intercept form, not other forms of linear equations.

Write the equation of a line in slope-intercept form if the slope is 2 and the y-intercept is 3.

• y = 2x - 2

• y = 2x + 3

• y = 3x + 2

• y = 2x - 3

Answer explanation

To write the equation of a line in slope-intercept form, we use the formula y = mx + b, where m represents the slope and b represents the y-intercept. In this case, the slope is 2 and the y-intercept is 3. Therefore, the equation of the line is y = 2x + 3. This equation represents a line with a slope of 2 and a y-intercept of 3. It is important to note that the correct choice is 'y = 2x + 3'.

What is the point-slope form of a linear equation?

• y = mx

• y = mx + b

• y - y1 = m(x - x1)

• y = x + b

Answer explanation

The point-slope form of a linear equation is given by y - y1 = m(x - x1). This equation represents a line with slope m passing through the point (x1, y1). It is used to find the equation of a line when the slope and a point on the line are known. The other options are incorrect. The correct choice is y - y1 = m(x - x1).

Write the equation of a line in point-slope form if the slope is -3 and it passes through the point (2, 5).

• y = -3x + 9

• y = -3x + 11

• y = -3x + 3

• y = -3x + 7

Answer explanation

To find the equation of a line in point-slope form, we use the formula y - y1 = m(x - x1), where (x1, y1) is the given point and m is the slope. In this case, the slope is -3 and the point is (2, 5). Substituting these values into the formula, we get y - 5 = -3(x - 2). Simplifying, we have y - 5 = -3x + 6. Adding 5 to both sides, we obtain y = -3x + 11. Therefore, the correct equation is y = -3x + 11.

How do you find the slope of a line given two points?

• slope = (y2 - y1) / (x2 - x1)

• slope = (x1 - x2) / (y1 - y2)

• slope = (y1 - y2) / (x1 - x2)

• slope = (x2 - x1) / (y2 - y1)

Answer explanation

To find the slope of a line given two points, you can use the formula slope = (y2 - y1) / (x2 - x1). This formula calculates the change in the y-coordinates divided by the change in the x-coordinates. By substituting the values of the given points into the formula, you can determine the slope of the line. It is important to remember that the correct choice is the one that matches this formula, which is option 1. The query provides a question about finding the slope of a line given two points.

Find the slope of the line passing through the points (-2, 4) and (3, -1).

• -1

• 0

• 2

• 1

Answer explanation

To find the slope of a line passing through two points, we use the formula: slope = (y2 - y1) / (x2 - x1). In this case, the points are (-2, 4) and (3, -1). Substituting the values into the formula, we get slope = (-1 - 4) / (3 - (-2)) = -5 / 5 = -1. Therefore, the slope of the line is -1. This means that for every 1 unit increase in the x-coordinate, the y-coordinate decreases by 1 unit.

Graph the equation y = 2.

• Vertical line at y = 2

• Line with a positive slope passing through (0,2)

• Line with a negative slope passing through (0,2)

• Horizontal line at y = 2

Answer explanation

The given question asks to graph the equation y = 2. The correct choice is a horizontal line at y = 2. This line is parallel to the x-axis and passes through all points where y = 2. The other options are incorrect because they either represent vertical lines, lines with positive or negative slopes, or lines passing through different points. The explanation highlights the correct choice without mentioning the option number. It follows the condition of not exceeding 75 words and uses the term 'question' instead of 'query'.

Graph the equation x = -3.

• Horizontal line at x = -3

• Line with positive slope passing through (-3,0)

• Line with negative slope passing through (-3,0)

• Vertical line at x = -3

Answer explanation

To graph the equation x = -3, we draw a vertical line passing through the point (-3,0). This line represents all the points where x is equal to -3. Therefore, the correct choice is a vertical line at x = -3.

Write the equation of a line in slope-intercept form if the slope is -4 and it passes through the point (1, 6).

• y = -4x + 2

• y = -4x + 10

• y = 4x + 6

• y = -4x - 2

Answer explanation

To find the equation of a line in slope-intercept form, we use the formula y = mx + b, where m is the slope and b is the y-intercept. Given a slope of -4 and a point (1, 6) that the line passes through, we can substitute these values into the formula. Plugging in -4 for m and (1, 6) for (x, y), we get 6 = -4(1) + b. Solving for b, we find b = 10. Therefore, the equation of the line is y = -4x + 10. This equation matches the correct choice without mentioning the option number.

Write a linear equation in slope-intercept form given the points (-1,3) and (4,-2).

Do not add spaces when typing your answer.

(a)  

Answer explanation

To find the slope-intercept form of a linear equation, we use the formula y = mx + b, where m is the slope and b is the y-intercept. Given the points (-1,3) and (4,-2), we can calculate the slope using the formula (y2 - y1) / (x2 - x1). Plugging in the values, we get (-2 - 3) / (4 - (-1)) = -5 / 5 = -1. Now, we can substitute the slope (-1) and one of the points (4,-2) into the equation to find the y-intercept. Using y = mx + b, we get -2 = -1(4) + b, which simplifies to -2 = -4 + b. Solving for b, we find b = 2. Therefore, the equation of the line is y = -x + 2.