Slope And Y-intercept Quiz: Test Your Knowledge

In the equation y = 3x - 2, the coefficient of x is the slope (m). So, the slope is 3.

The slope of a linear equation in the form y=mx+b is represented by the coefficient of x, which in this case is -2. Therefore, the slope of y=-2x+5 is -2.

The y-intercept of a linear equation represents the point where the line intersects the y-axis. In the equation y = 7 - 2x, the y-intercept can be found by setting x = 0 and solving for y. When x = 0, the equation becomes y = 7 - 2(0), which simplifies to y = 7. Therefore, the y-intercept is 7, and the point (0,7) represents this intersection with the y-axis.

The variable "m" represents the slope. In mathematics, slope refers to the steepness or incline of a line. It is calculated as the ratio of the vertical change (rise) to the horizontal change (run) between two points on the line. The variable "m" is commonly used to denote slope in equations of lines, such as y = mx + b, where "m" represents the slope and "b" represents the y-intercept.

If a line falls from the top left to the bottom right on a graph, it means that the line is sloping downwards. This indicates that the slope of the line is negative.

If the slope of a line is undefined, it means that the line is vertical. This is because the slope of a line is defined as the ratio of the change in y-coordinates to the change in x-coordinates. In a vertical line, the change in x-coordinates is always zero, which results in a denominator of zero in the slope formula. Since division by zero is undefined, the slope of a vertical line is also undefined. Therefore, if the slope of a line is undefined, it indicates that the line is vertical.

When the slope of a line is positive, it means that the line is increasing as it moves from left to right on the graph. This can be observed when the line rises from the bottom left to the top right.

The slope between two points (x1, y1) and (x2, y2) is given by the formula:

slope = (y2 - y1) / (x2 - x1)

In this case, the two points are (5, -5) and (-1, 7). Substituting these values into the formula, we get:

slope = (7 - (-5)) / (-1 - 5) = 12 / -6 = -2

If the slope of a line is zero, it means that the line is perfectly horizontal. This means that the line does not rise or fall, but remains at the same level throughout. In other words, the line will be parallel to the x-axis and will not have any vertical movement. Therefore, the correct answer is that the line will be horizontal.

To find the equation of a line passing through the points (-1, -2) and (-4, -12), you can use the point-slope form of the equation:



y - y1 = m(x - x1)



where (x1, y1) is one of the points, and m is the slope.



First, calculate the slope (m) using the two points:



m = (y2 - y1) / (x2 - x1)

m = (-12 - (-2)) / (-4 - (-1))

m = (-12 + 2) / (-4 + 1)

m = (-10) / (-3)

m = 10/3



Now that you have the slope, you can use one of the points, let's use (-1, -2):



y - (-2) = (10/3)(x - (-1))



Simplify:



y + 2 = (10/3)(x + 1)



Now, if you want the equation in standard form (Ax + By = C), you can multiply both sides by 3 to eliminate fractions:



3(y + 2) = 10(x + 1)



Expand:



3y + 6 = 10x + 10



Move terms around:



3y - 10x = 10 - 6



3y - 10x = 4



So, the equation of the line passing through (-1, -2) and (-4, -12) is:



3y - 10x = 4

The correct answer is "A constant change in y over the change in x." This answer accurately describes the concept of slope, which is the measure of how steep a line is. It indicates the rate at which the dependent variable (y) changes with respect to the independent variable (x). A constant change in y over the change in x means that for every unit increase in x, there is a consistent change in y. This is represented by the slope-intercept form of a linear equation, y=mx+b, where m represents the slope.

The y-intercept is the point where the line crosses the y-axis. To find the y-intercept, we can use the formula y = mx + b, where m is the slope and b is the y-intercept. We can find the slope by using the formula (y2 - y1) / (x2 - x1) with the given points (3, 7) and (2, 4). Plugging in the values, we get (4 - 7) / (2 - 3) = -3 / -1 = 3. Now, we can use the slope-intercept form to find the y-intercept. Plugging in the slope (3) and one of the points (2, 4) into the formula y = mx + b, we get 4 = 3(2) + b. Solving for b, we get b = -2. Therefore, the y-intercept is -2. Additionally, the point (0, -2) is also given as an answer, which confirms our calculation.

The equation of the line with a slope of -1/2 and passing through the point (4, 5) in slope-intercept form (y = mx + b) is expressed as follows: "y= - 1/2 x + 7," where 7 is the y-intercept.

In the slope-intercept form of a linear equation (y = mx + c), the coefficient 'm' represents the slope of the line. The slope indicates the steepness and direction of the line. A positive slope indicates an upward trend, while a negative slope indicates a downward trend. The greater the absolute value of 'm', the steeper the line.

The equation y = mx + c is the slope-intercept form of a linear equation, where 'm' represents the slope of the line and 'c' represents the y-intercept. The slope indicates the steepness and direction of the line, while the y-intercept is the point where the line crosses the y-axis. 1 This form is widely used to represent linear equations because it clearly shows the relationship between x and y values.