use the graph to derive the equation of the line in slope-intercept form. (1,3) and (0,-2)
To derive the equation of the line in slope-intercept form using the points (1,3) and (0,-2), we need to find the slope and the y-intercept of the line.
The slope (m) of a line can be calculated using the formula:
m = (change in y) / (change in x)
Given the points (1,3) and (0,-2), we can calculate the change in y and the change in x as follows:
change in y = 3 - (-2) = 5
change in x = 1 - 0 = 1
Now, we can calculate the slope:
m = (change in y) / (change in x) = 5 / 1 = 5
The slope-intercept form of a line is given by:
y = mx + b
where m is the slope and b is the y-intercept. To find the y-intercept, we can substitute one of the given points into the equation.
Let's substitute the point (1,3):
3 = 5(1) + b
3 = 5 + b
b = 3 - 5
b = -2
Now we have the slope (m = 5) and the y-intercept (b = -2). We can write the equation of the line in slope-intercept form:
y = 5x - 2
To find the equation of a line in slope-intercept form, we need to know the slope and the y-intercept of the line.
Given the points (1, 3) and (0, -2), we can find the slope using the formula:
slope (m) = (y2 - y1) / (x2 - x1)
Using the coordinates of the two points:
m = (-2 - 3) / (0 - 1)
m = -5 / -1
m = 5
Now that we have the slope, we can use one of the given points and the slope to find the y-intercept (b).
Let's use the point (0, -2) and substitute it into the slope-intercept form equation (y = mx + b):
-2 = 5(0) + b
-2 = b
So, the y-intercept (b) is -2.
Now we have both the slope (m = 5) and the y-intercept (b = -2), we can write the equation of the line in slope-intercept form:
y = mx + b
y = 5x - 2
Therefore, the equation of the line in slope-intercept form is y = 5x - 2.
To derive the equation of a line in slope-intercept form from the given coordinates (1,3) and (0,-2), we need to find the slope and the y-intercept.
The slope of a line can be calculated using the formula:
slope (m) = (change in y) / (change in x)
Let's calculate the slope using the given coordinates:
(change in y) = 3 - (-2) = 3 + 2 = 5
(change in x) = 1 - 0 = 1
slope (m) = 5 / 1 = 5
Now that we have the slope, we can proceed to find the y-intercept (b) using the slope-intercept form of a line:
y = mx + b
To calculate the y-intercept, substitute one of the given points into the equation:
Using the point (1,3):
3 = 5(1) + b
3 = 5 + b
b = 3 - 5
b = -2
Now we know the slope (m = 5) and the y-intercept (b = -2), we can write the equation of the line in slope-intercept form:
y = mx + b
y = 5x - 2
Therefore, the equation of the line in slope-intercept form is y = 5x - 2.