The image displays a coordinate plane with four plotted points, each labeled with its coordinates: (0, 3), (1, 5), (2, 7), and (3, 9). The task is to find the equation of the line that passes through these points.
To solve this, I will follow these steps:
1.
Verify they are collinear: Check if all four points lie on the same straight line by calculating the slope between consecutive points.
2.
Find the slope (m): Use any two points to calculate the slope of the line.
3.
Find the y-intercept (b): Use the slope and one of the points to find the y-intercept.
4.
Write the equation: Combine the slope and y-intercept into the slope-intercept form, $y = mx + b$.
Let's begin by verifying the points are collinear by calculating the slope between them.
- Slope between (0, 3) and (1, 5):
$m = \frac{5 - 3}{1 - 0} = \frac{2}{1} = 2$
- Slope between (1, 5) and (2, 7):
$m = \frac{7 - 5}{2 - 1} = \frac{2}{1} = 2$
- Slope between (2, 7) and (3, 9):
$m = \frac{9 - 7}{3 - 2} = \frac{2}{1} = 2$
Since the slope is consistently 2 between all consecutive points, they are indeed collinear and lie on the same straight line.
Now, I will use the point (0, 3) to find the y-intercept. The y-intercept is the value of $y$ when $x = 0$. Looking at the point (0, 3), we can see that when $x = 0$, $y = 3$. Therefore, the y-intercept $b$ is 3.
Finally, I can write the equation of the line using the slope $m = 2$ and the y-intercept $b = 3$.
The equation of the line is $y = 2x + 3$.
Parent Tip: Review the logic above to help your child master the concept of graphing linear equations formula.
