Question

The trend line that Sylvie has drawn for her graph goes through the points (5, 0) and (4, 3). What is the equation of the line?

Answer 1

y=-3x+15

1. Slope = -6.000/2.000 = -3.000

2. x-intercept = -15/3 = -5

3.y-intercept = 15/1 = 15.00000

Slope=rise over run

Calculate the Y-Intercept :

Notice that when x = 0 the value of y is 15/1 so this line "cuts" the y axis at y=15.00000

y-intercept = 15/1 = 15.00000

Calculate the X-Intercept :

When y = 0 the value of x is -5/1 Our line therefore "cuts" the x axis at x=-5.00000

x-intercept = -15/3 = -5

Calculate the Slope :

Slope is defined as the change in y divided by the change in x. We note that for x=0, the value of y is -15.000 and for x=2.000, the value of y is -21.000. So, for a change of 2.000 in x (The change in x is sometimes referred to as "RUN") we get a change of -21.000 - (-15.000) = -6.000 in y. (The change in y is sometimes referred to as "RISE" and the Slope is m = RISE / RUN)

Slope = -6.000/2.000 = -3.000

Geometric figure: Straight Line

Slope = -6.000/2.000 = -3.000

x-intercept = -15/3 = -5

y-intercept = 15/1 = 15.00000

Answer 2

y=-3x+15

Explanation:

To find the equation of the line, you need to find the slope and y intercept. The slope is pretty easy, as the line goes down by 3 after going up by 1. This means that the slope is -3/1=-3. The y intercept is also pretty easy, as you know that the line will increase by 3 every time you go back 1 to the left. 3*4=12, meaning that going back 4 will take you up 12. 3+12=15, meaning that the equation of the line is y=-3x+15. Hope this helps!