Question

Write the slope-intercept form of the equation of the line through the given points.

Answer 1

The slope-intercept form of a line is y = a + bx, where a is the y-intercept and b is the slope. To find the equation of a line with a slope of 3 and a y-intercept of 9, the equation is y = 9 + 3x. For the provided data, the line of best fit is y = 0.09x + 35.25.

Step-by-step explanation:

To write the slope-intercept form of the equation of a line through given points, you need to find the slope (b) and the y-intercept (a). The slope-intercept form of a linear equation is y = a + bx, where b is the slope and a is the y-intercept. The slope measures the steepness of the line, while the y-intercept is the point where the line crosses the y-axis.

Let's take an example where the slope of the line is 3, meaning that the line rises by 3 units for every 1 unit it moves horizontally. If the y-intercept is 9, the equation of the line is y = 9 + 3x.

In the context provided, to find the y-intercept (b), you can use the formula b = y - mx, where y and x are the coordinates of a point on the line and m is the slope. Using the sum of median x and y values provided, and a given slope (m ≈ 0.09), you calculate the y-intercept to be approximately 35.25, leading to the line of best fit equation y = 0.09x + 35.25.

Answer 2

y = 4x - 7 (Answer C)

Step-by-step explanation:

First find the slope of this line. Note that as we go from (2, 1) to (3, 5), x (the 'run') increases by 1 and y (the 'rise') increases by 4.

Thus, the slope, m, is

m = rise / run = 4/1, or m = 4.

Apply the point-slope form of the equation of a straight line, since we now have both the slope and two points on the line:

y - k = m(x - h) becomes y - 1 = 4(x - 2)

Solving for y, we get: y = 4x - 8 + 1, or y = 4x - 7 (Answer C)