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 slope-intercept form of the equation of a line, we need to determine the slope of the line and the y-intercept.
The slope of a line passing through two points, (x1, y1) and (x2, y2), is given by the formula:
slope = (y2 - y1) / (x2 - x1)
Using the given points (-2, -4) and (2, 4), we can calculate the slope:
slope = (4 - (-4)) / (2 - (-2))
= (4 + 4) / (2 + 2)
= 8 / 4
= 2
So, the slope of the line passing through the given points is 2.
Now, we can use the point-slope form of the equation of a line, which is:
y - y1 = m(x - x1)
where m is the slope of the line and (x1, y1) is one of the given points.
Let's use the first point (-2, -4):
y - (-4) = 2(x - (-2))
y + 4 = 2(x + 2)
Now, let's simplify the equation:
y + 4 = 2x + 4
Subtract 4 from both sides:
y = 2x + 4 - 4
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 the points (-2, -4) and (2, 4), we can follow the following steps:
Step 1: Find the slope (m) of the line.
The slope (m) can be found using the formula:
m = (y2 - y1) / (x2 - x1)
Let's label the coordinates as follows:
(x1, y1) = (-2, -4)
(x2, y2) = (2, 4)
Substituting the values into the formula, we have:
m = (4 - (-4)) / (2 - (-2))
m = 8 / 4
m = 2
Step 2: Use the slope-intercept form, which is given by y = mx + b, where m is the slope and b is the y-intercept.
Step 3: Find the y-intercept (b).
To find the y-intercept (b), we can substitute the coordinates of one of the given points into the equation (y = mx + b) and solve for b.
Let's use the point (2, 4) to find the y-intercept:
4 = 2 * 2 + b
4 = 4 + b
b = 4 - 4
b = 0
Step 4: Write the equation of the line.
Using the values we found for m (slope) and b (y-intercept), we can write the equation of the line:
y = 2x + 0
Simplifying, we get:
y = 2x
Therefore, 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, we will use the formula:
y = mx + b
where:
- "m" represents the slope of the line, and
- "b" represents the y-intercept.
To find the slope (m), we can use the formula:
m = (y2 - y1) / (x2 - x1)
Let's calculate the slope using the given points (-2,-4) and (2,4):
m = (4 - (-4)) / (2 - (-2))
= 8 / 4
= 2
Now that we have the slope (m), we can substitute it into the slope-intercept form equation:
y = 2x + b
To find the y-intercept (b), we can choose either of the given points and substitute the coordinates into the equation. Let's use the point (-2,-4):
-4 = 2(-2) + b
-4 = -4 + b
b = 0
Therefore, the y-intercept (b) is 0.
Now we can write the final equation with the slope (m) and y-intercept (b):
y = 2x + 0
y = 2x
Hence, the slope-intercept form of the equation of the line passing through the points (-2,-4) and (2,4) is y = 2x.