Graphing Equations Quick Check

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Question
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 negative 3 x minus 4

y=3x−4
y equals 3 x minus 4

y=3x+4
y equals 3 x plus 4

3x−y=4
3 x minus y equals 4

Answer 1

To find the equation of the line in slope-intercept form (y = mx + b), we first need to find the slope (m) and the y-intercept (b).

The slope (m) is the change in y divided by the change in x. Given two points (0, -4) and (1, -1), we can calculate the slope as follows:

m = (-1 - (-4)) / (1 - 0) = (3) / (1) = 3

Now, we know our line has the form y = 3x + b.

To find the y-intercept (b), we can use one of the given points. Since the point (0, -4) is on the line, we can replace x and y in our equation with these values:

-4 = 3(0) + b

-4 = 0 + b

-4 = b

Now, we have both the slope and y-intercept, so the equation of the line in slope-intercept form is:

y = 3x - 4