Activity 15 SB

Front

What is the slope (m) of a linear graph?

Back

The slope (m) of a linear graph represents the rate of change of the y-coordinate with respect to the x-coordinate. It is calculated as the rise over run, or the change in y divided by the change in x.

Front

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

Back

The slope-intercept form of a linear equation is given by the formula y = mx + b, where m is the slope and b is the y-intercept.

Front

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

Back

To find the equation of a line given two points (x1, y1) and (x2, y2), first calculate the slope (m) using m = (y2 - y1) / (x2 - x1). Then use the point-slope form y - y1 = m(x - x1) to derive the equation.

Front

What is the y-intercept of a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis. It is represented by the value of y when x = 0 in the equation of the line.

Front

What does it mean if a line has an undefined slope?

Back

A line has an undefined slope if it is vertical, meaning it goes straight up and down. In this case, the x-coordinate remains constant while the y-coordinate changes.

Front

How do you convert the standard form of a linear equation to slope-intercept form?

Back

To convert from standard form Ax + By = C to slope-intercept form y = mx + b, solve for y by isolating it on one side of the equation.

Front

What is the significance of the slope in real-world applications?

Back

The slope in real-world applications indicates the relationship between two variables, such as speed (distance over time) or cost (price per unit). It helps in understanding trends and making predictions.

Front

What is the formula for calculating the slope between two points?

Back

The formula for calculating the slope (m) between two points (x1, y1) and (x2, y2) is m = (y2 - y1) / (x2 - x1).

Front

What is the graphical representation of the equation 6x - 5y = 15?

Back

To graph the equation 6x - 5y = 15, first convert it to slope-intercept form (y = mx + b) to identify the slope and y-intercept.

Front

What does a positive slope indicate about a linear graph?

Back

A positive slope indicates that as the x-value increases, the y-value also increases, showing a direct relationship between the two variables.