Algebra function

Question

Line f1 has a slope of -5/4 and passes through the point (4,2)

Answer 1

In this case, it seems like the question provides information for you to generate an equation. Considering that the slope contains no variable, we can assert that this is a linear equation.

Before we begin, we should pick out our equation and determine what each component represents.

Our equation, in this case, would be:

y = mx+b

y = value generated from the equation

m = Slope

x = Position on the X-axis

b = Y-intercept

Consider that the equation provides us with three of the four missing variables:

1. The slope (m) = -(5/4)
2. The x value (x) = 4
3. The corresponding y value (y) = 2

To generate this equation, we would like the y-intercept, which is not provided. Note that to generate a linear function, we would need the slope and the y-intercept so that we can get any coordinate that would fit the function.

Solution:

Step 1: Fill in known variables into the equation

2 = -(5/4) x 4 + b

Step 2: Simplify where possible

2 = -((5 x 4)/4) + b --> 2 = -5 + b

Step 3: Isolate and solve for the variable

2 = -5 + b

+5 +5

7 = b

Step 4: Insert the acquired Y- intercept into the equation with only the value for the slope

y = -(5/4)x + 7

These steps will get most questions like this done quite effectively. Practice some more with additional questions and it should come naturally. Good luck!

Answer 2

2= (-5/4)(4) +b

2=-5 +b

b=2+5=7

y= -5x/4+7

or

5x+4y= 28