Final answer:
The slope of the line passing through points (1, 0.1) and (7, 26.8) is calculated using the slope formula, resulting in a slope of 4.5. For the second line with a given point (0,4) and slope of -1, the equation of the line is y = -1x + 4, which is in slope-intercept form.
Step-by-step explanation:
To find the slope of a line passing through two points, you can use the formula:
slope (m) = ∆y / ∆x = (y2 - y1) / (x2 - x1)
In the provided example, we have two points, Point 1: (1, 0.1) and Point 2: (7, 26.8). Applying the slope formula, we get:
slope (m) = (26.8 - 0.1) / (7 - 1) = 26.7 / 6 = 4.45, which can be rounded to 4.5. Thus, the correct answer is option b. 4.5.
Remember that when the slope is constant, any two points on the line can be used to find the slope. It is generally more accurate to use two points far apart to minimize any errors in reading data from the graph. If the second line passes through the point (0,4) and has a slope of -1, this informs us that for every one unit increase in x, the value of y decreases by 1. This could be written as an equation of the line: y = -1x + 4. An equation in slope-intercept form is expressed as y = mx + b, where m is the slope and b is the y-intercept. In the example of the line passing through (0,4) with a slope of -1, the equation is in slope-intercept form.