Answer:
Use the two ordered pairs to find the slope, m.
Then substitute the slope, and one set of ordered pairs into y = mx + b to solve for b.
Step-by-step explanation:
I will provide an example in order to help you understand what each missing term means in the context of the given topic.
Example:
The common math problems involving linear functions are often stated as,
"Find the equation of the line that passes through points (0, 4) and (1, 6)."
Step 1:
Since we are given two points, we can use these to solve for the slope using the following slope formula:
[tex]\displaystyle\mathsf{Slope\:(m) =\:\frac{y_2 - y_1}{x_2 - x_1}}[/tex]
Let (x₁, y₁) = (0, 4)
(x₂, y₂) = (1, 6)
Substitute these values into the slope formula:
[tex]\displaystyle\mathsf{Slope\:(m) =\:\frac{y_2 - y_1}{x_2 - x_1}\:=\:\frac{6-4}{1-0}\:=\:\frac{2}{1}\:=\:2}[/tex]
Therefore, the slope of the line is 2.
Solve for the y-intercept:
Next, we must determine the value of the y-intercept, which is the point on the graph where it crosses the y-axis. Whenever the line crosses the y-axis, it means that its coordinates will be (0, b ) ⇒ the y-coordinate represents the value of the y-intercept, b, in the slope-intercept form, y = mx + b.
Step 2:
Using the slope, m = 2, and one of the given points, (1, 6), substitute these values into the slope-intercept form to solve for the value of y-intercept, b:
y = mx + b
6 = 2( 1 ) + b
6 = 2 + b
Subtract 2 from both sides to isolate b:
6 - 2 = 2 - 2 + b
4 = b
Thus, the y-intercept, b = 4.
Now that we have our slope, m = 2, and the y-intercept, b = 4, then we can establish the following linear function as: y = 2x + 4.
Summary:
As highlighted in Steps 1 and 2 of our given example, it shows how these sequence of steps fits in with the missing terms in your assignment.
- We used the two ordered pairs to solve for the slope.
- Once we have our slope, we used this value and one of the given ordered pairs to solve for the value of the y-intercept, b, by plugging in these values into the slope-intercept form, y = mx + b.
