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.
To find the equation of the line in slope-intercept form, we need to determine the slope and the y-intercept of the line.
First, let's find the slope of the line using the two given points. The formula for calculating the slope (m) is:
m = (y2 - y1) / (x2 - x1)
Using the points (0, 4) and (1, 8) in the above formula, we have:
m = (8 - 4) / (1 - 0)
m = 4 / 1
m = 4
Now, we need to determine the y-intercept (b) of the line. We can use the slope-intercept form of a line:
y = mx + b
We already have the slope (m = 4), and we can substitute one of the given points (0, 4) into the equation to find b:
4 = 4(0) + b
4 = 0 + b
b = 4
Therefore, the equation of the line in slope-intercept form is y = 4x + 4.
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.
To find the equation of a line in slope-intercept form, we need to determine the slope (m) and the y-intercept (b).
Given the points (0, 4) and (1, 8), we can calculate the slope using the formula: m = (y2 - y1) / (x2 - x1)
Let's substitute the values into the formula:
m = (8 - 4) / (1 - 0)
m = 4 / 1
m = 4
So the slope of the line is 4.
Next, we can use the slope-intercept form of a line, which is y = mx + b. We can substitute one of the known points (0, 4) into the equation and solve for b.
We have the equation:
4 = 4(0) + b
This simplifies to:
4 = 0 + b
4 = b
Therefore, the y-intercept of the line is 4.
Putting the values of m and b into the slope-intercept form equation, we have:
y = 4x + 4
Therefore, the equation of the line in slope-intercept form is y = 4x + 4.
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 2 right parenthesis and left parenthesis 1 comma negative 1 right parenthesis.
Write the equation of the line in slope-intercept form.
To find the equation of the line in slope-intercept form, we need to determine the slope and the y-intercept of the line.
First, let's find the slope of the line using the two given points. The formula for calculating the slope (m) is:
m = (y2 - y1) / (x2 - x1)
Using the points (0, 2) and (1, -1) in the above formula, we have:
m = (-1 - 2) / (1 - 0)
m = -3 / 1
m = -3
Now, we need to determine the y-intercept (b) of the line. We can use the slope-intercept form of a line:
y = mx + b
We already have the slope (m = -3), and we can substitute one of the given points (0, 2) into the equation to find b:
2 = -3(0) + b
2 = 0 + b
b = 2
Therefore, the equation of the line in slope-intercept form is y = -3x + 2.
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 on both ends is plotted on the graph. The line passes through the plotted points left parenthesis 0 comma negative 2 right parenthesis and left parenthesis 3 comma 0 right parenthesis.
Write the equation of the line in slope-intercept form.
To find the equation of the line in slope-intercept form, we need to determine the slope and the y-intercept of the line.
First, let's find the slope of the line using the two given points. The formula for calculating the slope (m) is:
m = (y2 - y1) / (x2 - x1)
Using the points (0, -2) and (3, 0) in the above formula, we have:
m = (0 - (-2)) / (3 - 0)
m = 2 / 3
Now, we need to determine the y-intercept (b) of the line. We can use the slope-intercept form of a line:
y = mx + b
We already have the slope (m = 2/3), and we can substitute one of the given points (0, -2) into the equation to find b:
-2 = (2/3)(0) + b
-2 = 0 + b
b = -2
Therefore, the equation of the line in slope-intercept form is y = (2/3)x - 2.