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-line
Dot on 4 which is located on y-line
Dot on 5 which is located on x-line
Dot on 10 which is located on x-line
To find the equation of a line in slope-intercept form, we need to determine the slope and the y-coordinate of the y-intercept.
The slope (m) can be found using the formula:
m = (y2 - y1) / (x2 - x1)
Using the given points (-10,-5) and (5,10):
m = (10 - (-5)) / (5 - (-10))
m = 15 / 15
m = 1
Now we can determine the y-intercept (b) using the point (4,0):
0 = m(4) + b
0 = 1(4) + b
0 = 4 + b
b = -4
Therefore, the equation of the line in slope-intercept form is:
y = mx + b
y = 1x - 4
y = x - 4
To find the equation of the line in slope-intercept form, we need to determine the slope and y-intercept.
Given information:
-10 on the x-line
Dot on -5 on the x-line
Dot on 4 on the y-line
Dot on 5 on the x-line
Dot on 10 on the x-line
First, let's find the slope.
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 choose the points (-5, 0) and (4, 0) that lie on the x-axis.
Change in y = 0 - 0 = 0
Change in x = 4 - (-5) = 4 + 5 = 9
Slope (m) = Change in y / Change in x = 0/9 = 0
Next, let's find the y-intercept (b).
Since the line passes through the point (0, -10) on the x-axis, the y-intercept is -10.
Now we can write the equation of the line in slope-intercept form.
The slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.
Substituting the values we found:
y = 0x - 10
y = -10
Therefore, the equation of the line in fully simplified slope-intercept form is y = -10.
To find the equation of a line in slope-intercept form (y = mx + b), we need to find the slope (m) and the y-intercept (b).
Given the following points:
- (-10, 0) on the x-axis
- (-5, 4) on the coordinate plane
- (5, 10) on the coordinate plane
- (10, 0) on the x-axis
Step 1: Find the slope (m)
The slope (m) between two points (x1, y1) and (x2, y2) is given by the formula:
m = (y2 - y1) / (x2 - x1)
Let's find the slope between the points (-10, 0) and (-5, 4).
m = (4 - 0) / (-5 - (-10))
= 4 / (-5 + 10)
= 4 / 5
So, the slope (m) is 4/5.
Step 2: Find the y-intercept (b)
To find the y-intercept (b), we can use any of the given points. Let's use the point (5, 10).
Using the slope-intercept form:
y = mx + b
Substitute the slope (m) and the coordinates (x, y) of the point (5, 10):
10 = (4/5)(5) + b
10 = 4 + b
To isolate b, we subtract 4 from both sides:
10 - 4 = b
b = 6
So, the y-intercept (b) is 6.
Step 3: Write the equation
Now that we have the slope (m = 4/5) and the y-intercept (b = 6), we can write the equation of the line in slope-intercept form:
y = (4/5)x + 6
Therefore, the equation of the line in fully simplified slope-intercept form is y = (4/5)x + 6.