Final answer:
The slope of the line passing through points (1, 0.1) and (7, 26.8) is calculated using the slope formula, yielding a value of 4.45. This value corresponds to option b. 4.5. The slope represents the rate of change of y with respect to x in a linear equation, and is consistent along a straight line. The correct option is C .
Step-by-step explanation:
To find the slope of a line passing through any two points, we need to use the formula for slope which is:
m = (y2 - y1) / (x2 - x1)
Where ‘m’ denotes the slope, (x1, y1) are the coordinates of the first point, and (x2, y2) are the coordinates of the second point.
For the given points, Point 1: (1, 0.1) and Point 2: (7, 26.8), let’s calculate the slope:
m = (26.8 - 0.1) / (7 - 1)
m = 26.7 / 6
m = 4.45
Thus, the slope of the line passing through the points (1, 0.1) and (7, 26.8) is 4.45, which corresponds to option b. 4.5.
When dealing with linear equations like y = mx + b, ‘m’ represents the slope and ‘b’ represents the y-intercept. Looking at Figure A1, we see that the slope is constant for a linear equation, meaning that for every unit increase in x, y increases by a consistent amount, which is the slope value. For instance, a slope of 3 indicates for every increase of 1 on the horizontal axis, there is a rise of 3 on the vertical axis.
The equations provided in Practice Test 4, options A, B, and C, are examples of linear equations because they can be written in the form y = mx + b, where 'm' is the slope and 'b' is the y-intercept.