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:
Let (x₁, y₁) = (0, 4)
(x₂, y₂) = (1, 6)
Substitute these values into the slope formula:
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.
