Write the equation of the line fully simplified slope-intercept form. 12 11 10 -12-11-10-9-5-7-6-5-4-3-2-1, 3456789012 -LO 11
The Correct Answer and Explanation is:
To help you effectively, I need to clarify a few things first. It looks like your message includes a lot of numbers that are out of context. The actual math question seems to be:
“Write the equation of the line fully simplified in slope-intercept form. Provide the correct answer and a 300-word explanation.”
But to do this correctly, I need at least two points that the line passes through, or information such as the slope and y-intercept.
Let me show you how to solve this problem with an example using two points:
Suppose we are given the points (2, 3) and (4, 7).
Step 1: Find the slope (m)
The slope formula is: m=y2−y1x2−x1m = \frac{y_2 – y_1}{x_2 – x_1}
Plugging in the points: m=7−34−2=42=2m = \frac{7 – 3}{4 – 2} = \frac{4}{2} = 2
Step 2: Use point-slope form
Now that we have the slope m=2m = 2, we can use one of the points (say, (2, 3)) and plug it into the point-slope form: y−y1=m(x−x1)y – y_1 = m(x – x_1) y−3=2(x−2)y – 3 = 2(x – 2)
Step 3: Convert to slope-intercept form (y = mx + b)
Distribute the 2: y−3=2x−4y – 3 = 2x – 4
Add 3 to both sides: y=2x−1y = 2x – 1
Final Answer:
y=2x−1\boxed{y = 2x – 1}
Explanation:
The slope-intercept form of a linear equation is written as y=mx+by = mx + b, where mm is the slope of the line, and bb is the y-intercept—the point where the line crosses the y-axis. To write a linear equation in this form, you need either the slope and y-intercept directly or two points from the line.
When given two points, the first step is to calculate the slope (m) using the formula m=y2−y1x2−x1m = \frac{y_2 – y_1}{x_2 – x_1}. This formula calculates the rate of change between the two points—essentially, how steep the line is. In our example, the points (2, 3) and (4, 7) were used, and the slope was found to be 2.
Next, we use the point-slope form y−y1=m(x−x1)y – y_1 = m(x – x_1), which helps construct the equation when we know a point and the slope. After plugging in the slope and one of the points, we simplify and convert the equation into slope-intercept form.
Finally, we simplify the equation to get it into the form y=mx+by = mx + b. This is important because it’s the most commonly used form and easily shows both the slope and y-intercept, which are key characteristics of the line’s behavior on a grap
