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 on 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 3 comma 0 right parenthesis.
Write the equation of the line in slope-intercept form.
(1 point)
The slope-intercept form of a line is y = mx + b, where m is the slope and b is the y-intercept.
To find the slope of the line, we can use the coordinates of the two points given: (0, -2) and (3, 0).
The slope (m) can be calculated using the formula: m = (y2 - y1) / (x2 - x1).
Using the coordinates, we have:
m = (0 - (-2)) / (3 - 0) = 2/3.
Now that we have the slope, we can use one of the given points to find the y-intercept (b).
Let's use the point (0, -2).
We substitute the values into the equation y = mx + b:
-2 = (2/3)(0) + b
-2 = b
So, the y-intercept is -2.
Now we can write the equation of the line in slope-intercept form:
y = 2/3x - 2.
To find the equation of a line in slope-intercept form (y = mx + b), we need to determine the slope (m) and the y-intercept (b).
First, let's find the slope (m) using the given points (0, -2) and (3, 0).
m = (y2 - y1) / (x2 - x1)
= (0 - (-2)) / (3 - 0)
= 2 / 3
Next, since the line passes through the point (3, 0), we can substitute this point into the equation to solve for the y-intercept (b).
0 = (2/3)(3) + b
0 = 2 + b
b = -2
Therefore, the equation of the line in slope-intercept form is:
y = (2/3)x - 2