To find the slope-intercept form of a line that passes through two points, we start by identifying the points given: (3, 4) and (5, 16).
The slope-intercept form of a line is represented as:
y = mx + b
where:
- m is the slope of the line.
- b is the y-intercept where the line crosses the y-axis.
First, we need to calculate the slope (m) using the formula:
m = (y2 – y1) / (x2 – x1)
Substituting the coordinates of the points:
m = (16 – 4) / (5 – 3)
m = 12 / 2
m = 6
Now that we have the slope, we can use one of the points to solve for b. Let’s use the point (3, 4):
Substituting into the slope-intercept equation:
y = mx + b
4 = 6(3) + b
4 = 18 + b
Now, isolate b:
b = 4 – 18
b = -14
Now we can combine our slope and y-intercept into the slope-intercept form of the equation:
y = 6x – 14
In summary, the slope-intercept form of the equation of the line that passes through the points (3, 4) and (5, 16) is:
y = 6x – 14