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 minus 4
y=3x+4
y equals 3 x plus 4
y=−3x−4
y equals negative 3 x minus 4
3x−y=4
3 x minus y equals 4
To determine the equation of the line in slope-intercept form, we can first find the slope of the line. The slope is found by finding the difference in the y-coordinates divided by the difference in the x-coordinates of the two given points on the line.
Using the points (0, -4) and (1, -1):
slope = (change in y) / (change in x)
slope = (-1 - (-4)) / (1 - 0)
slope = (3) / (1)
slope = 3
Now that we have the slope, we can use the point-slope form of a linear equation, where the slope is represented by m and a point on the line is represented by (x1, y1):
y - y1 = m(x - x1)
Using the point (0, -4), the equation becomes:
y - (-4) = 3(x - 0)
Simplifying:
y + 4 = 3x
To convert the equation to slope-intercept form (y = mx + b), which is the desired form, we isolate y:
y = 3x - 4
Therefore, the equation of the line in slope-intercept form is y = 3x - 4.
pick one of the responses
y=3x-4
To derive the equation of the line in slope-intercept form using the given graph, we need to determine the slope and the y-intercept.
From the plotted points (0, -4) and (1, -1), we can calculate the slope using the formula:
slope (m) = (change in y) / (change in x)
= (-1 - -4) / (1 - 0)
= 3 / 1
= 3
Now that we have the slope (m), we can use the point-slope form of a linear equation:
y - y₁ = m(x - x₁)
For this equation, we can use the point (0, -4) as the point (x₁, y₁).
So, substituting the values:
y - (-4) = 3(x - 0)
y + 4 = 3x
Now, we can rearrange the equation to the slope-intercept form (y = mx + b) by isolating y:
y = 3x - 4
Therefore, the equation of the line in slope-intercept form is:
y = 3x - 4.