(3,0)(0,-2) write the equation of the line in slope-intercept form.
To write the equation of a line in slope-intercept form, we need to find the slope and the y-intercept.
Given the two points (3,0) and (0,-2), we can find the slope using the formula:
slope = (change in y) / (change in x)
slope = (0 - (-2)) / (3 - 0)
= 2 / 3
The slope of the line is 2/3.
Now, let's find the y-intercept using one of the points. We'll use the point (3,0).
Using the slope-intercept form of a line: y = mx + b, where m is the slope and b is the y-intercept, we can substitute the values we calculated.
0 = (2/3)(3) + b
0 = 2 + b
b = -2
The y-intercept of the line is -2.
Therefore, the equation of the line in slope-intercept form is:
y = (2/3)x - 2
To write the equation of a line in slope-intercept form, we need to find the slope (m) and the y-intercept (b).
The slope (m) represents the rate at which the line inclines or declines. It can be calculated using the formula:
m = (y2 - y1) / (x2 - x1)
Given two points on the line: (3, 0) and (0, -2), we can use these coordinates to calculate the slope:
m = (0 - (-2)) / (3 - 0)
m = 2 / 3
Now that we have the slope (m), we can find the y-intercept (b). The y-intercept is the value of y when x is 0, which can be identified with one of the given points.
Using the point (3, 0):
0 = m * 3 + b
0 = (2/3) * 3 + b
0 = 2 + b
To solve for b, subtract 2 from both sides:
b = -2
So, the slope (m) is 2/3 and the y-intercept (b) is -2.
Now we can write the equation of the line in slope-intercept form:
y = mx + b
Replacing m and b with their values:
y = (2/3)x - 2
Therefore, the equation of the line in slope-intercept form is y = (2/3)x - 2.
To write the equation of the line in slope-intercept form, we need to find the slope (m) and the y-intercept (b).
Step 1: Find the slope (m):
The slope (m) can be calculated using the formula:
m = (y2 - y1) / (x2 - x1)
Using the given points (3, 0) and (0, -2), we can substitute the values into the formula:
m = (-2 - 0) / (0 - 3)
m = -2 / -3
m = 2/3
So, the slope (m) of the line is 2/3.
Step 2: Find the y-intercept (b):
The y-intercept (b) is the value of y when x is 0. We can substitute the values of one of the given points into the equation y = mx + b and solve for b.
Let's use the point (3, 0):
0 = (2/3)(3) + b
0 = 2 + b
b = -2
So, the y-intercept (b) of the line is -2.
Step 3: Write the equation of the line in slope-intercept form:
Now that we have the slope (m) and the y-intercept (b), we can write the equation of the line in slope-intercept form, which is given by:
y = mx + b
Substituting the values of m and b that we found:
y = (2/3)x - 2
Therefore, the equation of the line in slope-intercept form is y = (2/3)x - 2.