Write the equation of the line in fully simplified slope-intercept form.
Positive line on -10 on x-line
Dot on -5 which is located on x-axis and 2 which on the y-axis
Dot on 4 which is located on y-line
Dot on 5 which is located on x-line and 6 which on the y-axis
Dot on 10 which is located on x-line and 7 which on the y-axis
To find the equation of the line, we first need to find the slope (m) and the y-intercept (b).
The slope (m) is given by the difference in y-coordinates divided by the difference in x-coordinates between two points on the line. Let's consider the points (-5,0) and (5,6). The difference in y-coordinates is 6-0=6, and the difference in x-coordinates is 5-(-5)=10. Therefore, the slope (m) is 6/10 = 3/5.
Now that we have the slope (m), we can use it to find the y-intercept (b). Let's substitute the coordinates (5,6) into the slope-intercept form equation (y=mx+b) and solve for b:
6 = (3/5)(5) + b
6 = 3 + b
b = 6-3
b = 3
Therefore, the equation of the line is y = (3/5)x + 3.
To find the equation of the line in slope-intercept form, we need to determine the slope (m) and the y-intercept (b).
Given that the line passes through the points (-5, 0) and (10, 7), we can calculate the slope using the formula:
m = (y2 - y1) / (x2 - x1)
Substituting the coordinates of the two points:
m = (7 - 0) / (10 - (-5))
m = 7 / 15
So, the slope (m) is 7/15.
Next, we can determine the y-intercept (b) by substituting the coordinates of one of the points (let's use (-5, 0) in this case) and the slope (m) into the slope-intercept form: y = mx + b.
0 = (7/15)(-5) + b
0 = -7/3 + b
To solve for b, we add 7/3 to both sides:
7/3 = b
So, the y-intercept (b) is 7/3.
Finally, we can write the equation of the line in slope-intercept form:
y = (7/15)x + 7/3
To find the equation of a line in slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept, we need to first find the slope (m) and then substitute the values of one of the given points (x, y) into the equation to solve for the y-intercept (b).
Given points:
Point A: (-5, 2)
Point B: (4, y)
Point C: (5, 6)
Point D: (10, 7)
Step 1: Find the slope (m):
To find the slope, we use the formula: m = (y2 - y1) / (x2 - x1)
Using the points A and C:
m = (6 - 2) / (5 - (-5))
m = 4 / 10
m = 2/5
Step 2: Substitute the coordinates of one of the points into the slope-intercept form equation (y = mx + b) and solve for b:
Using the coordinates of point A:
2 = (2/5)(-5) + b
2 = -2 + b
b = 2 + 2
b = 4
So the y-intercept (b) is 4.
Step 3: Write the equation in slope-intercept form (y = mx + b):
Substituting the values of m and b into the equation:
y = (2/5)x + 4
Therefore, the equation of the line in fully simplified slope-intercept form is y = (2/5)x + 4.