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 4 right parenthesis and left parenthesis 1 comma negative 1 right parenthesis.
Using the graph, derive the equation of the line in slope-intercept form.
(1 point)
Responses
y=3x+4
y equals 3 x plus 4
3x−y=4
3 x minus y equals 4
y=−3x−4
y equals negative 3 x minus 4
y=3x−4
y = 3x - 4
are u sure
Apologies for the confusion in my previous response. Looking at the given information, the line passes through the points (0, -4) and (1, -1). To find the slope of the line, we can use the formula:
m = (y2 - y1) / (x2 - x1)
Substituting the coordinates of the two points into the formula:
m = (-1 - (-4)) / (1 - 0)
m = 3/1
m = 3
Now that we have the slope (m = 3), we can use the point-slope form of a linear equation:
y - y1 = m(x - x1)
Substituting the coordinates of one of the points (0, -4):
y - (-4) = 3(x - 0)
y + 4 = 3x
y = 3x - 4
Therefore, the equation of the line in slope-intercept form is:
y = 3x - 4
To derive the equation of the line in slope-intercept form, we need to find the slope and the y-intercept.
First, let's find the slope using the two plotted points:
Slope (m) = (change in y) / (change in x)
From the graph, we can determine that the change in y is 1 unit (from -4 to -1) and the change in x is also 1 unit (from 0 to 1).
So, the slope is:
m = (1) / (1) = 1
Next, let's find the y-intercept by determining the value of y when x is 0.
From the graph, we can see that the line passes through the point (0, -4).
So, the y-intercept is -4.
Now, we can write the equation of the line in slope-intercept form, which is y = mx + b, where m represents the slope and b represents the y-intercept.
Plugging in the values, we have:
y = 1x - 4
Simplifying, we get:
y = x - 4
Therefore, the equation of the line in slope-intercept form is y = x - 4.