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.
To find the equation of the line in slope-intercept form, we need to determine the slope and the y-intercept.
First, let's find the slope using the two given points: (0, -2) and (3, 0).
The slope (m) is given by the formula:
m = (y₂ - y₁) / (x₂ - x₁)
Substituting the coordinates, we have:
m = (0 - (-2)) / (3 - 0)
m = (0 + 2) / (3)
m = 2/3
Now, we can use the slope-intercept form of a line, which is:
y = mx + b
Where "m" is the slope and "b" is the y-intercept.
To find the y-intercept (b), we can use one of the given points. Let's use (0, -2):
-2 = (2/3)(0) + b
-2 = 0 + b
b = -2
Therefore, the equation of the line in slope-intercept form is:
y = (2/3)x - 2
To write the equation of a line in slope-intercept form (y = mx + b), we need to find the slope (m) and the y-intercept (b) of the line.
Given that the line passes through the points (0, -2) and (3, 0), we can find the slope using the formula:
m = (y₂ - y₁) / (x₂ - x₁)
Substituting the coordinates (x₁, y₁) = (0, -2) and (x₂, y₂) = (3, 0), we have:
m = (0 - (-2)) / (3 - 0)
m = 2 / 3
Therefore, the slope (m) of the line is 2/3.
Now, we can use the point-slope form of a line (y - y₁ = m(x - x₁)) to find the equation. We can choose either of the given points, let's use the point (0, -2):
y - (-2) = (2/3)(x - 0)
y + 2 = (2/3)x
Finally, let's rearrange the equation into slope-intercept form by isolating y:
y = (2/3)x - 2
Therefore, the equation of the line in slope-intercept form is y = (2/3)x - 2.