An equation in slope-intercept form follows a specific format. In this case, we are asked to write our equation in function notation.
f(x)= mx+ b
For an equation in this form, m is the slope and b is the y-intercept.
We have also been given two points in function notation. To write these points as coordinate pairs, remember that the input x is the x-coordinate and the output f(x) is the y-coordinate.
f( x)&= y ⇔ ( x, y)
f( 10)&= 5 ⇔ ( 10, 5)
f( 2)&= -3 ⇔ ( 2, -3)
Let's use the given points to calculate m and b. We will start by substituting the points into the Slope Formula.
A slope of 1 means that for every 1 horizontal step in the positive direction, we take 1 vertical step in the positive direction. Now that we know the slope, we can write a partial version of the equation.
f(x)= 1 x+ b ⇒ f(x)=x+b
To complete the equation, we also need to determine the y-intercept, b. Since we know that the given points will satisfy the equation, we can substitute one of them into the equation to solve for b. Let's use ( 10, 5).
