(-2,-3), (-1,-1), (0,1), (1,3), (2,5) what is the equation of the line in slope intercept form
To find the equation of a line in slope-intercept form (y = mx + b), we need to first calculate the slope (m) and then determine the y-intercept (b).
The slope formula is given by:
m = (y₂ - y₁) / (x₂ - x₁)
Let's consider the points (-2, -3) and (2, 5) to calculate the slope:
m = (5 - (-3)) / (2 - (-2))
= 8 / 4
= 2
So, the slope of the line is 2.
Now, we can select one of the points to substitute into the slope-intercept form equation. Let's choose the point (0, 1):
1 = 2(0) + b
1 = b
Therefore, the y-intercept (b) is 1.
Now we can write the equation of the line:
y = mx + b
y = 2x + 1
Hence, the equation of the line in slope-intercept form is y = 2x + 1.
To find the equation of the line in slope-intercept form, we need to determine the slope (m) and the y-intercept (b).
We can use the formula for calculating the slope between two points:
m = (y2 - y1) / (x2 - x1)
Let's choose any two points from the given set of points. We will use (-2, -3) and (2, 5).
m = (5 - (-3)) / (2 - (-2))
m = 8 / 4
m = 2
Now that we have the slope, we can use the point-slope form to find the equation:
y - y1 = m(x - x1)
Using the point (-2, -3) and the slope (2):
y - (-3) = 2(x - (-2))
y + 3 = 2(x + 2)
Next, we simplify the equation:
y + 3 = 2x + 4
Lastly, we rearrange the equation to slope-intercept form (y = mx + b):
y = 2x + 4 - 3
y = 2x + 1
Therefore, the equation of the line in slope-intercept form is y = 2x + 1.
To find the equation of a line in slope-intercept form (y = mx + b), we need to determine the values of the slope (m) and the y-intercept (b).
The slope (m) is calculated as the change in y divided by the change in x between any two points on the line. Let's select two points from the given coordinates, for example, (-2, -3) and (2, 5):
Change in y = 5 - (-3) = 8
Change in x = 2 - (-2) = 4
So, the slope (m) is 8/4 = 2.
Now that we have the slope (m), we can proceed to find the y-intercept (b). We can choose any point on the line to substitute into the slope-intercept form. Let's use the point (-2, -3):
y = mx + b
-3 = 2(-2) + b
-3 = -4 + b
To solve for b, add 4 to both sides of the equation:
b = -3 + 4
b = 1
Therefore, the equation of the line in slope-intercept form is y = 2x + 1.