Question

Write the equation of the linear relationship in slope-intercept form, using decimals as needed.

x 25 35 45 55
y 92.5 87.5 82.5 77.5

Answer 1

The linear relationship between x and y, given the points provided, is represented by the equation y = -0.5x + 105, where -0.5 is the slope and 105 is the y-intercept.

Step-by-step explanation:

To find the equation of the linear relationship between x and y in slope-intercept form, we first calculate the slope of the line. The slope, represented by m, is the change in y divided by the change in x. Looking at the given points, we can calculate the slope using any two points from the dataset. For example, using the points (25, 92.5) and (35, 87.5), the slope m is (87.5 - 92.5) / (35 - 25) = -5 / 10 = -0.5.

Now that we have the slope, we need to find the y-intercept. We can use the fact that the equation of a line in slope-intercept form is y = mx + b, where b is the y-intercept. Plugging one of the points into the equation along with our calculated slope, say (25, 92.5), gives us 92.5 = (-0.5)(25) + b. Solving for b, we get b = 92.5 + 12.5 = 105.

Thus, the equation of the line in slope-intercept form is y = -0.5x + 105.

Answer 2

To find the linear equation, calculate the slope using two points and then solve for the y-intercept using one point and the slope. The slope-intercept form of the equation with the calculated slope and y-intercept is y = -0.5x + 105.

Step-by-step explanation:

The student is asking to write the equation of a linear relationship in slope-intercept form, which is y = mx + b, using the given x and y values. To find the slope (m), we can use any two points from the set. For example, using the points (25, 92.5) and (35, 87.5), the slope can be calculated as m = (87.5 - 92.5) / (35 - 25) = -5 / 10 = -0.5.

This means for every increase of 1 in x, y decreases by 0.5. To find the y-intercept (b), we can substitute any point into the equation along with our slope.

Let's use the point (25, 92.5): 92.5 = -0.5(25) + b, which simplifies to 92.5 = -12.5 + b, and then b = 92.5 + 12.5 = 105. Therefore, the slope-intercept form of the equation is y = -0.5x + 105.

The complete question is: content loaded

Write the equation of the linear relationship in slope-intercept form, using decimals as needed.

x 25 35 45 55

y 92.5 87.5 82.5 77.5 is: