Use the image to answer the question.
An illustration of a coordinate plane with four quadrants shows the x-axis ranging from negative 9 to 9 and the y-axis ranging from negative 11 to 11 in increments of 1. A solid upward line with arrows at both ends is plotted on the graph. The line passes through the plotted points left parenthesis 0 comma negative 2 right parenthesis and left parenthesis 1 comma 3 right parenthesis.
Use the graph to derive the equation of the line in slope-intercept form.
(1 point)
Based on the information given, we can see that the line passes through the points (0, -2) and (1, 3). We can use these two points to find the slope of the line.
The slope (m) of a line passing through two points (x1, y1) and (x2, y2) can be found using the formula:
m = (y2 - y1) / (x2 - x1)
In this case, plugging in the coordinates (0, -2) and (1, 3):
m = (3 - (-2)) / (1 - 0)
m = 5 / 1
m = 5
Now that we have the slope, we can use the slope-intercept form of a linear equation, y = mx + b, where m is the slope and b is the y-intercept. We can substitute the slope (m = 5) and one of the points (0, -2) into the equation and solve for b.
-2 = 5(0) + b
-2 = 0 + b
b = -2
Now we have the slope (m = 5) and the y-intercept (b = -2), so the equation of the line in slope-intercept form is:
y = 5x - 2