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 downward line with arrows at both ends is plotted on the graph. The line passes through the plotted points left parenthesis 0 comma 1 right parenthesis and left parenthesis 1 comma negative 4 right parenthesis.
Write the equation of the line in slope-intercept form.
(1 point)
Responses
y=−5x−1
y equals negative 5 x minus 1
y=−5x+1
y equals negative 5 x plus 1
−5x−y=−1
negative 5 x minus y equals negative 1
y=5x+1
y=5x+1
are you sure
Apologies for the confusion. I made a mistake in my previous response. Since the line passes through the points (0,1) and (1,-4), we can find the slope of the line using the formula:
m = (y2 - y1) / (x2 - x1) = (-4 - 1) / (1 - 0) = -5/1 = -5.
Next, we can choose one of the given points (0,1) and substitute its coordinates and the slope into the slope-intercept form of a line, which is y = mx + b.
Using (0,1) and a slope of -5, we have:
1 = -5(0) + b.
Simplifying, we find that b = 1.
Therefore, the equation of the line in slope-intercept form is:
y = -5x + 1.
So the correct answer is y = -5x + 1.
To find the equation of the line in slope-intercept form, we need to determine the slope (m) and the y-intercept (b).
From the given points (0, 1) and (1, -4), we can find the slope (m) using the formula:
m = (y2 - y1) / (x2 - x1)
Substituting the values, we get:
m = (-4 - 1) / (1 - 0) = -5/1 = -5
Now that we have the slope, we can use the point-slope form of the equation:
y - y1 = m(x - x1)
Substituting the values from one of the given points (0, 1), we get:
y - 1 = -5(x - 0)
Simplifying this equation, we get:
y - 1 = -5x
To rewrite it in slope-intercept form (y = mx + b), we isolate y:
y = -5x + 1
Therefore, the equation of the line in slope-intercept form is:
y = -5x + 1.