To find the slope-intercept form of the equation of the line that passes through the points (1, 3) and (3, 7), we need to first determine the slope of the line.
The slope (m) is calculated using the formula:
m = (y2 – y1) / (x2 – x1)
Substituting the points (x1, y1) = (1, 3) and (x2, y2) = (3, 7), we get:
m = (7 – 3) / (3 – 1) = 4 / 2 = 2
Now that we have the slope, we can use one of the points to find the y-intercept (b). We can use the slope-intercept form of the equation, which is:
y = mx + b
Plugging in the slope and one of the points, let’s use (1, 3):
3 = 2(1) + b
This simplifies to:
3 = 2 + b
Subtracting 2 from both sides gives:
b = 1
Now we can write the equation of the line in slope-intercept form:
y = 2x + 1
This means the line that passes through the points (1, 3) and (3, 7) has the slope-intercept form of the equation y = 2x + 1.