c What is measured to determine the slope and distance between two points?
A
aSlope: m=4/5
Equation: y=4/5x+9/5
B
b d=sqrt(41)
C
c See solution
Practice makes perfect
a Let's plot the points and graph the line.
To find the line's slope, we have to divide the vertical distance by the horizontal distance between the two points on the line. Let's find these measures.
When we have found the vertical and horizontal distance between the two points, the slope can be determined.
m=Δ y/Δ x ⇔ m=4/5
When we know the slope, we have half of what we need to write the full equation in slope-intercept form.
y=4/5x+b
To complete the equation, we also need to know the y-intercept b. We can find this value by substituting one of the known points in the equation and solving for b.
c One similarity between the calculations is that the slope measures the vertical and horizontal distance between two points which is also part of the Distance Formula. d=sqrt(( x_2-x_1)^2+(y_2-y_1)^2)
The difference is what is done with these measurements. The Distance Formula uses them to calculate the length of a segment while the Slope Formula uses them to determine a line's steepness.
