The slope-intercept form of a line is expressed as y = mx + b, where m represents the slope of the line and b is the y-intercept. To find this equation for the line that passes through the points (1, 3) and (3, 7), we’ll first need to calculate the slope (m).
To calculate the slope, use the formula:
m = (y2 – y1) / (x2 – x1)
In our case, let:
- (x1, y1) = (1, 3)
- (x2, y2) = (3, 7)
Plugging these values into the slope formula gives us:
m = (7 – 3) / (3 – 1) = 4 / 2 = 2
Now that we have the slope m = 2, we can substitute it into the slope-intercept equation:
y = 2x + b
Next, we need to find the y-intercept b. We can do this by substituting one of our points into the equation. Let’s use the point (1, 3):
Substituting into the equation:
3 = 2(1) + b
This simplifies to:
3 = 2 + b
Solving for b gives:
b = 3 – 2 = 1
Now we have both the slope and the y-intercept:
m = 2 and b = 1
Finally, we can write the slope-intercept form of the equation of the line:
y = 2x + 1
So, the slope-intercept form of the equation for the line that passes through the points (1, 3) and (3, 7) is y = 2x + 1.