Write the slope-intercept form of the equation of a line that passes through the points (-2,-4) and (2,4). Enter your answer below and show all the steps that you used to solve this problem for full credit.
To find the equation of a line passing through two points (-2,-4) and (2,4), we can use the slope-intercept form of a linear equation, which is given by y = mx + b, where m is the slope of the line and b is the y-intercept.
Step 1: Find the slope (m) of the line.
The slope (m) can be found using the formula:
m = (y2 - y1) / (x2 - x1)
Substitute the coordinates of the two points into the formula:
m = (4 - (-4)) / (2 - (-2))
m = 8 / 4
m = 2
Step 2: Substitute the slope (m) and one of the points into the slope-intercept form (y = mx + b) to solve for b.
We can use either of the two points. Let's use the point (-2,-4).
y = mx + b
-4 = 2*(-2) + b
-4 = -4 + b
b = -4 + 4
b = 0
Step 3: Write the equation using the slope (m) and y-intercept (b).
The equation of the line is:
y = 2x + 0
Simplifying, we can write:
y = 2x
So, the slope-intercept form of the equation of the line that passes through the points (-2,-4) and (2,4) is y = 2x.
To find the slope-intercept form of the equation of a line passing through two given points, we need to find the slope (m) and the y-intercept (b).
Step 1: Calculate the slope (m)
The slope (m) of a line passing through two points (x₁, y₁) and (x₂, y₂) can be calculated using the formula:
m = (y₂ - y₁) / (x₂ - x₁)
Using the given points (-2, -4) and (2, 4), we can substitute the values into the formula:
m = (4 - (-4)) / (2 - (-2))
m = 8 / 4
m = 2
Step 2: Find the y-intercept (b)
To find the y-intercept (b), we can use the slope-intercept form of a line, which is y = mx + b. Since the line passes through the point (2, 4), we can substitute the values into the equation:
4 = 2(2) + b
4 = 4 + b
b = 4 - 4
b = 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 the equation of a line that passes through two given points, we can use the slope formula:
m = (y2 - y1) / (x2 - x1)
Let's label the first point as (x1, y1) = (-2, -4) and the second point as (x2, y2) = (2, 4). The slope (m) can be calculated as:
m = (4 - (-4)) / (2 - (-2))
= 8 / 4
= 2
Now that we have the slope, we can substitute it into the slope-intercept form of a linear equation:
y = mx + b
where m is the slope and b is the y-intercept that we need to find.
Using one of the given points, (-2, -4), we can substitute the values into the equation to solve for b:
-4 = 2(-2) + b
-4 = -4 + b
b = -4 + 4
b = 0
Therefore, the equation of the line in slope-intercept form is:
y = 2x + 0
However, the term "+0" is unnecessary, so the simplified form is:
y = 2x