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 4 right parenthesis and left parenthesis 1 comma 8 right parenthesis.
Derive the equation of the line in slope-intercept form.
(1 point)
To find the equation of the line in slope-intercept form, we need to determine the slope (m) and the y-intercept (b).
First, let's find the slope (m) using the given points (0, 4) and (1, 8).
m = (y2 - y1) / (x2 - x1)
m = (8 - 4) / (1 - 0)
m = 4/1
m = 4
Now, we can use the point-slope form of a line to find the equation.
y - y1 = m(x - x1)
Using point (0, 4):
y - 4 = 4(x - 0)
y - 4 = 4x
To convert this to slope-intercept form, we can isolate y:
y = 4x + 4
Therefore, the equation of the line in slope-intercept form is y = 4x + 4.
To derive the equation of the line in slope-intercept form, we need to determine the slope and the y-intercept.
We are given two points on the line: (0, 4) and (1, 8).
Slope (m) can be calculated using the formula:
m = (y2 - y1) / (x2 - x1)
Taking the points (0, 4) and (1, 8), we have:
m = (8 - 4) / (1 - 0)
m = 4
So, the slope of the line is 4.
Using the slope-intercept form of a line (y = mx + b), we can substitute the slope (4) and one of the given points (0, 4) to find the y-intercept (b).
4 = 4(0) + b
4 = b
Therefore, the y-intercept is 4.
Putting it all together, the equation of the line in slope-intercept form is:
y = 4x + 4