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.
a. 3x−y=4
b. y=3x+4
c. y=−3x−4
d. y=3x−4
To find the equation of the line in slope-intercept form (y=mx+b), we first need to calculate the slope. The slope (m) can be found using the formula:
m = (y2 - y1)/(x2 - x1)
where (x1, y1) = (0, -4) and (x2, y2) = (1, -1).
m = (-1 - (-4))/(1 - 0)
m = 3/1
m = 3
Now that we have the slope, we can use one of the points (0, -4) to find the y-intercept (b). Plugging the values into the equation y = mx + b:
-4 = 3(0) + b
b = -4
Therefore, the equation of the line in slope-intercept form is y = 3x - 4. This matches option d.
So, the correct answer is:
d. y = 3x - 4