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)
y = x + (-2)
To derive the equation of the line in slope-intercept form, we need to find the slope and the y-intercept of the line using the two given points.
First, let's calculate the slope (m) using the formula:
m = (y2 - y1) / (x2 - x1)
where (x1, y1) = (0, -2) and (x2, y2) = (1, 3).
m = (3 - (-2)) / (1 - 0)
m = 5/1
m = 5
So, the slope of the line is 5.
Next, let's substitute one of the given points and the slope into the slope-intercept form equation: y = mx + b.
Using the point (1, 3):
3 = 5(1) + b
3 = 5 + b
b = 3 - 5
b = -2
Therefore, the y-intercept (b) is -2.
Finally, substituting the values for m and b into the equation y = mx + b, we get the equation of the line in slope-intercept form:
y = 5x - 2
To determine the equation of the line in slope-intercept form from the given graph, we'll need to find the slope and y-intercept.
From the image, we can see that the line passes through the points (0, -2) and (1, 3).
To find the slope, we'll use the formula:
slope (m) = (change in y)/(change in x)
The change in y = 3 - (-2) = 5
The change in x = 1 - 0 = 1
Therefore, the slope (m) = 5/1 = 5.
Now that we have the slope, we can use the point-slope form of a linear equation:
y - y₁ = m(x - x₁)
We'll choose the point (0, -2) as our reference point.
Plugging in the values, we get:
y - (-2) = 5(x - 0)
y + 2 = 5x
To rewrite the equation in slope-intercept form, we'll isolate y:
y = 5x - 2
So, the equation of the line in slope-intercept form is y = 5x - 2.