I need help understanding this.

Question

Item 8

Item 8

Item 8

Item 8

A line passes through point A (10,15). A second point on the line has an x-value that is 125% of the x-value of point and a y-value that is 75% of the y-value of point . Use point to write an equation of the line in point-slope form.

Answer 1

Hi Lydia,

The first thing we can do is find out where that second point is. It has an x-value that is 125% of point A's x-value, which is 10. What's 125% of 10? 12.5, which you can calculate a number of ways. How about the y-value: it's 75% of point A's y-value, which is 15. 75% of 15 is 11 1⁄4 or 11.25 (I got that by changing 75% to 3/4 and multiplying that by 15). Okay, now we have our second point, (12.5, 11.25).

In order to complete our line, we need to find out how steep the change from point A to our new point is. In other words, the slope. Calculate that by taking the difference in our y-values, and dividing by the difference in our x-values, so the slope m = (y_B − y_A) / (x_B − x_A) = (11.25 −15) / (12.5 - 10) = -3.75 / 2.5 = -3/2.

Great! We have the slope, and we have a point A that we can use in our point-slope form equation. Recall point slope form is y − y₁ = m(x − x₁), where (x₁, y₁) is a point on the line, like point A. Plugging in, we get:

y − 15 = -3/2(x − 10)

So there you have it! If you need clarification or have any other questions, please don't hesitate to ask :)

Answer 2

y-15 = (-2)(x-10)

125% of 10 = (10)5/4 = 50/4 = 12.5

75% of 15 = 45/4=11.25

the point (45/4,50/4)= (11.25,2.5) is another point on the line

first point (10,15) = (40/4,60/4)

slope = (y1-y2)/(x1-x2)

slope = (60/4-50/4)/(40/4-45/4) =10/-5 = -2

y-12.5 = -(2)(x-11.25) or

y-15 = -(2)(x-10)

both in point slope form

they're equivalent

subtract one from the other

5 = -(2)(22,5-20)=-2(2.5) = 5