Exercise 106 Page 192

To write the equation, we have to find its slope m and y-intercept b. When we know this we can write the equation in slope-intercept form. y= mx+ b In addition to the y-intercept we know the angle at which the line increases. Let's demonstrate this with a graph. Note that a line's slope is defined as the vertical change when you move 1 unit in the positive horizontal direction. Therefore, from the y-intercept we will also draw a slope triangle with a horizontal side of 1 and an angle of 25^(∘).

If we can find the value of m we can get the slope of the line. Since we know the adjacent leg to the given angle, by using the tangent ratio we can find the value of m.

tan θ = Opposite/Adjacent

SubstituteValues

Substitute values

tan 25^(∘) = m/1

▼

Solve for m

DivByOne

a/1=a

tan 25^(∘) = m

RearrangeEqn

Rearrange equation

m=tan 25^(∘)

UseCalc

Use a calculator

m = 0.46630...

RoundDec

Round to 2 decimal place(s)

m ≈ 0.47

The slope is about 0.47. With this information we can complete the equation. y≈ 0.47x+4