To find the equation of a line that passes through two points, we need to use the slope-intercept form of the equation of a line, which is given by:
y = mx + b
where m is the slope of the line and b is the y-intercept.
First, let’s calculate the slope (m) of the line using the formula:
m = (y2 – y1) / (x2 – x1)
Given the points (1, 7) and (2, 10):
- (x1, y1) = (1, 7)
- (x2, y2) = (2, 10)
Now plug in the values:
m = (10 – 7) / (2 – 1)
m = 3 / 1 = 3
Now that we have the slope (m = 3), we can use one of the points to find b. Let’s use the point (1, 7):
y = mx + b
7 = 3(1) + b
7 = 3 + b
b = 7 – 3 = 4
Now we have both the slope and the y-intercept. Putting it all together, the equation of the line is:
y = 3x + 4
In conclusion, the equation of the line that passes through the points (1, 7) and (2, 10) is y = 3x + 4.