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
The slope of the line can be found by using the two given points on the line:
slope = (change in y) / (change in x) = (-1 - (-4)) / (1 - 0) = 3/1 = 3
Using the point-slope form (y - y1) = m(x - x1) with one of the given points, we can write:
(y - (-4)) = 3(x - 0)
Simplifying and solving for y, we get:
y = 3x - 4
Therefore, the correct answer is y=3x−4, or "y equals 3 x minus 4".
hi
Well, from the graph it looks like the line goes up from the point (0,-4) to the point (1,-1). So it has a positive slope. Let's calculate it using the slope formula:
slope = (y2 - y1) / (x2 - x1) = (-1 - (-4)) / (1 - 0) = 3/1 = 3.
Now, we can use the point-slope form of a linear equation:
y - y1 = m(x - x1),
where (x1, y1) are the coordinates of one of the points on the line and m is the slope. Let's use the point (1,-1):
y - (-1) = 3(x - 1),
y + 1 = 3x - 3,
y = 3x - 3 - 1,
y = 3x - 4.
So, 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 determine the slope of the line and the y-intercept.
First, we can find the slope of the line using the two given points (0, -4) and (1, -1).
Slope (m) is given by the formula:
m = (y2 - y1) / (x2 - x1)
Substituting the values, we get:
m = (-1 - (-4)) / (1 - 0)
m = (-1 + 4) / (1)
m = 3/1
m = 3
Next, we can determine the y-intercept (b) by substituting one of the given points into the equation y = mx + b.
Using the point (0, -4):
-4 = 3(0) + b
-4 = 0 + b
b = -4
Therefore, the equation of the line in slope-intercept form is:
y = 3x - 4.
To determine the equation of the line in slope-intercept form, we need to identify the slope (m) and the y-intercept (b).
From the image, we can see that the line passes through the points (0, -4) and (1, -1).
First, let's calculate the slope (m) using the formula: m = (change in y) / (change in x).
The change in y is -1 - (-4) = 3, and the change in x is 1 - 0 = 1.
Therefore, the slope (m) is 3/1 = 3.
Next, we can use the slope-intercept form of a linear equation, y = mx + b, and substitute the values of the slope (m) and one of the points (0, -4) into the equation to find the y-intercept (b).
Using the point (0, -4):
-4 = 3(0) + b
-4 = 0 + b
b = -4
Finally, we can substitute the values of the slope (m = 3) and the y-intercept (b = -4) into the equation y = mx + b:
y = 3x - 4
Therefore, the correct answer is:
y = 3x - 4