Algebra

Estimate the equation of the line of best fit using two points on the line: (6, 15) and (9, 21). y = 3x + 3 y = 2x + 3 y = 2x - 3 y = x + 3

Step-by-step solution with explanation

Final Answer

Step-by-step solution

1

Find the slope using two points

Slope tells us how steep the line is. We subtract the y-values and divide by the difference in x-values to find how much y changes for every 1 unit increase in x.
2

Write slope-intercept form with known slope

Now that we know the slope is 2, we plug it into the slope-intercept form y = mx + b. We still need to find b, the y-intercept.
3

Plug in one point to solve for b

We substitute the point (6, 15) into the equation. Solving for b gives us 3. You can verify with the second point: 21 = 2(9) + 3 = 18 + 3 = 21 ✓
4

Write the final equation of the line

We now have both the slope (m = 2) and the y-intercept (b = 3). This matches one of the answer choices exactly.

Understanding this problem

Learning Insight

The slope-intercept form y = mx + b is built on two key ideas: the slope m describes the rate of change (rise over run), and b is where the line crosses the y-axis. Two points are all you ever need to define a unique straight line.

Quick Tip

Always check your equation with BOTH given points. If both work, you got it right. If only one works, recheck your slope calculation first.

Common Mistake

Students often subtract the coordinates in the wrong order when finding slope — like writing (9 - 6) on top and (21 - 15) on the bottom. Always keep x-differences on the bottom and y-differences on top, in the same order.