(1, 3) (0,-2)
Using the graph, derive the equation of the line in slope-intercept form.
To find the equation of the line in slope-intercept form (y = mx + b) using the given points (1, 3) and (0, -2), we first need to find the slope (m) of the line.
The formula for finding the slope of a line passing through two points (x1, y1) and (x2, y2) is:
m = (y2 - y1) / (x2 - x1)
Plugging in the values from the given points:
m = (-2 - 3) / (0 - 1)
m = -5 / -1
m = 5
Now that we have the slope, we can use one of the points to find the y-intercept (b) of the line. Let's use the point (1, 3).
Using the slope-intercept form (y = mx + b), we can substitute the slope (m = 5), x = 1, and y = 3 into the equation:
3 = 5(1) + b
3 = 5 + b
b = 3 - 5
b = -2
Now that we have both the slope (m = 5) and the y-intercept (b = -2), we can write the equation of the line in slope-intercept form:
y = 5x - 2
Therefore, the equation of the line in slope-intercept form that passes through the points (1, 3) and (0, -2) is y = 5x - 2.