Exercise 31 Page 175

As we can see, the original solver tries to write the equation in point-slope form. Notice that the given two points, g( 5)= 4 and g( 3)= 10, are in function notation. To start, let's write these points as coordinate pairs. Remember that the input x is the x-coordinate and the output g(x) is the y-coordinate. g( x)= y ⇔ ( x, y) g( 5)= 4 ⇔ ( 5, 4) g( 3)= 10 ⇔ ( 3, 10) Now, we are able to write an equation for function g in slope-intercept form. However, we cannot determine the y-intercept of the equation from the given points. Therefore, we will follow two steps.

1. We will first find the slope of the equation by using the Slope Formula.
2. Next, we will write the equation in point-slope form.

Finding the Slope

We know that the line of function g passes through the points ( 5, 4) and ( 3, 10). Let's substitute these points into the Slope Formula and find the slope.

m = y_2-y_1/x_2-x_1

SubstitutePoints

Substitute ( 5,4) & ( 3,10)

m=10- 4/3- 5

SubTerms

Subtract terms

m=-6/2

CalcQuot

Calculate quotient

m=-3

The slope of the line is -3. The original solver has also found the slope as -3. Therefore, there is not error in this step.

Point-Slope Form

We know the slope of the line and two points that are on the line. We can choose one of these points and write the equation of the line. Let's choose the point ( 5, 4) as the original solver has. y- 4= -3(x- 5) In this step, the original solver has applied the point-slope form. Therefore, s/he has an incorrect equation at the end.