Write the slope intercept form of the equations of a line that passes through the points (-2,-4) and (2,4). Show all the steps you used.
To find the equation of a line in slope-intercept form, we need to find the slope and the y-intercept.
Step 1: Find the slope (m) of the line using the formula:
m = (y2 - y1) / (x2 - x1) [Point-slope form]
m = (4 - (-4)) / (2 - (-2))
m = 8 / 4
m = 2
Step 2: Use the slope-intercept form of a line, y = mx + b, and substitute the coordinate values of one of the given points to find the y-intercept (b).
Let's substitute the coordinates of the point (2, 4):
4 = 2(2) + b
4 = 4 + b
b = 4 - 4
b = 0
Step 3: Write the equation using the slope (m) and the y-intercept (b).
The equation is: y = 2x + 0
Since the y-intercept is 0, we can simplify the equation to y = 2x.
Therefore, the equation of the line that passes through the points (-2, -4) and (2, 4) is y = 2x.
To find the equation of a line in slope-intercept form given two points, we need to follow these steps:
Step 1: Calculate the slope of the line.
Step 2: Use the slope and one of the given points to find the y-intercept.
Step 3: Write the equation in slope-intercept form.
Let's go through each step:
Step 1: Calculate the slope of the line.
The slope (m) of a line passing through two points (x1, y1) and (x2, y2) is given by the formula:
m = (y2 - y1) / (x2 - x1)
Using the two points (-2, -4) and (2, 4), we can substitute the values into the slope formula:
m = (4 - (-4)) / (2 - (-2))
= (4 + 4) / (2 + 2)
= 8 / 4
= 2
So, the slope (m) of the line is 2.
Step 2: Use the slope and one of the given points to find the y-intercept.
Using the slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept, we can substitute the slope (m = 2) and one of the given points. Let's use (-2, -4):
-4 = 2(-2) + b
-4 = -4 + b
b = -4 + 4
b = 0
So, the y-intercept (b) is 0.
Step 3: Write the equation in slope-intercept form.
Now that we have the slope (m = 2) and the y-intercept (b = 0), we can write the equation in slope-intercept form:
y = mx + b
y = 2x + 0
y = 2x
Therefore, the slope-intercept form of the equation of the line passing through the points (-2, -4) and (2, 4) is y = 2x.
To find the slope-intercept form of a line passing through two given points, we first need to find the slope of the line.
Step 1: Find the slope (m)
The formula to calculate the slope (m) of a line passing through two points, (x₁, y₁) and (x₂, y₂), is given by:
m = (y₂ - y₁) / (x₂ - x₁)
Using the given points (-2,-4) and (2,4), we substitute the coordinates into the formula:
m = (4 - (-4)) / (2 - (-2))
= (4 + 4) / (2 + 2)
= 8 / 4
= 2
So, the slope (m) of the line passing through the given points is 2.
Step 2: Use the slope-intercept form
The slope-intercept form of a linear equation is: y = mx + b, where m is the slope and b is the y-intercept.
Since we have the slope (m) as 2, we can plug in this value along with one of the points to find the y-intercept (b).
Let's use the point (-2,-4):
-4 = 2(-2) + b
-4 = -4 + b
b = 0
Now that we have the slope (m = 2) and the y-intercept (b = 0), we can write the equation in slope-intercept form:
y = 2x + 0
Simplifying, we get:
y = 2x
Therefore, the slope-intercept form of the equation of the line passing through the points (-2,-4) and (2,4) is y = 2x.