a In the slope triangle, you are given the opposite and adjacent legs.
B
b Create a slope triangle with an angle of 45^(∘) and an adjacent side of 1 unit.
C
c If you combine the equations you get a system of equations.
A
a ≈ 71.57^(∘)
B
b y=x+3
C
c (1,4)
Practice makes perfect
a The line is written in slope-intercept form which means it follows a certain format.
y= mx+ b
In this form, m is the slope and b is the y-intercept. To graph the given equation, we will start at the y-intercept, (0,1), and then use the line's slope to plot a second point.
Finally, to find the slope angle, θ, we will use the tangent ratio on the slope triangle.
b To write the equation, we have to find it's 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 with which the line increases. Let's demonstrate this in 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 45^(∘).
If we can find m, we can get the slope of the line. Since we know the adjacent leg to the reference angle, we can use the tangent ratio to find the value of m.
