Slope-Intercept Form: y=x+1 Standard From: x-y=- 1
Practice makes perfect
We want to write an equation in slope-intercept form representing the weight of a box depending on number of balls it contains. Let y be the weight of the box containing x balls.
y=mx+b
Here, m is the slope and b is the y-intercept. We know that a box with 4 balls weighs 5lb and a box with 10 balls weighs 11lb.
x
y
4
5
10
11
We can use this information to find the slope and the y-intercept. Let's start by determining the slope using the Slope Formula.
m=y_2-y_1/x_2-x_1
We will use ( 4,5) and ( 10,11) as (x_1,y_2) and (x_2,y_2), respectively.
The slope is equal to 1. Now we can form our partial equation.
y=1x+b ⇔ y=x+b
To find the value of b, we will substitute one of the points into the partial equation and solve it for b. Let's use the point ( 4, 5).
The y-intercept is equal to 1. We can finish writing the equation.
y=x+1
Finally, we have to rewrite the equation in standard form using integercoefficients.
Ax+By=C
Since all coefficients of our equation, y=x+1, are already integers, we will only have to rearrange the terms.
