Question

Table:

Arm Span (inches Height (inches)
58 60
49 47
51 55
19 25
37 39
44 45
47 49
36 35
41. 40
46 50
58 61




Predict the line of best fit.

Write the equation of the line of best fit using slope-intercept formula y = mx + b

What does the slope of the line represent with the context of my graph and what does the y-intercept represent?

Test the residualsnof two other points to determine how well the line of best fit models the data.

Use the line of best fit to describe the data correlation.

Using line of bets fit using slope-intercept formula, approximately how tall is a person who's Arm Span is 66 inches?

According to the line of bets fit, what is the arm span of a 74 inch-tall person?​

Answer 1

Answer:

y = mx + b is the slope intercept form of writing the equation of a straight line. In the equation 'y = mx + b', 'b' is the point, where the line intersects the 'y axis' and 'm' denotes the slope of the line. The slope or gradient of a line describes how steep a line is. It can have either a positive or a negative value. When a standard form of a linear equation is of the form Ax + By = C, where 'x' and 'y' and 'C' are variables and 'A', 'B' are constants, the slope intercept form is the most preferred way of expressing a straight line due to its simplicity, as it is very easy to find the slope and the 'y intercept' from the given equation.

Step-by-step explanation:

Meaning of y = mx + b

y = mx + b is the slope-intercept form of a staight line. In the equation y = mx + b for a straight line, m is called the slope of the line and b is the y-intercept of a line. y = mx+b, where 

y ⇒  how far up or down is the line, 

x  ⇒ how far along is the line,   

b ⇒ the value of y when x = 0 and

m ⇒ how steep the line is.

This is determined by m = (difference in y coordinates)/ (difference in x coordinates). Note that difference in y coordinates is indicated as rise or fall and difference in x coordinates is indicated as run.



How To Find y = mx + b?

y = mx + b is the formula used to find the equation of a straight line, when we know the slope(m) and the y-intercept (b) of the line. To determine m, we apply a formula based on the calculations. Let's derive this formula using the equation for the slope of a line. Let us consider a line whose slope is 'm' and whose y-intercept is 'b'. Let (x,y) be any other random point on the line whose coordinates are not known. We obtain the graph as follows.



We know that the equation for the slope of a line in the slope-intercept form is y = mx+b

Rewriting this, we get m = (y-b) / x 

Thus the formula to find m = change in y/ change in x



Let us derive the formula to find the value of the slope if two points (x1,y1)(x1,y1) and (x2,y2)(x2,y2) on the straight line are known. Then we have y1=mx1+by1=mx1+b and y2=mx2+by2=mx2+b

We know that, slope = change in y/ change in x

Substituting the values of y1 and y2, we get y2−y1x2−x1=(mx2+b)−(mx1+b)x2−x1=mx2−mx1x2−x1=m(x2−x1)x2−x1