Question

Use the ordered pairs (1,39) and (5,65) to find the equation of a line that approximates the data. Express your answer in slope intercept form. (If necessary, round the slope to the nearest hundredth and the y-intercept to the nearest whole number.)

Answer 1

Hello there. To solve this question, we'll have to remember how to find the equation of a line given two points that it passes through.

Given the points (x1, y1) and (x2, y2), the equation of the line assumes the form y = mx + b, where m is the slope of the line and b is y-intercept.

The slope m can be calculated by the formula:

$m=\frac{y_2-y_1_{}_{}}{x_2-x_1}$

Plugging in the values for the ordered pairs given, the slope is:

$m=\frac{65-39}{5-1}=\frac{26}{4}=6.5$

Putting this value in the equation of the line, we have:

y = 6.5x + b

Now, to find b, we can use any of the points given

39 = 6.5 * 1 + b

39 = 6.5 + b

Subtract 6.5 from both sides of the equation

b = 32.5

As we want to round the y-intercept to the nearest whole number, that is 32, we have that the equation of the line is:

y = 6.5x + 32