(1, 3) (0, -2) use that graph to derive the equation of the line in slope-intercept form.
To derive the equation of the line in slope-intercept form, we need to find the slope and the y-intercept.
Given the points (1, 3) and (0, -2), we can find the slope using the slope formula:
slope = (change in y)/(change in x) = (3 - (-2))/(1 - 0) = (3 + 2)/(1) = 5/1 = 5
Next, we can use the slope-intercept form of a line, y = mx + b, where m is the slope and b is the y-intercept.
Substituting the given slope of 5 and the coordinates of one point (1, 3) into the equation, we can solve for b:
3 = 5(1) + b
3 = 5 + b
b = 3 - 5
b = -2
Therefore, the equation of the line in slope-intercept form is y = 5x - 2.
To find the equation of the line in slope-intercept form (y = mx + b), we need to determine the slope (m) and the y-intercept (b) using the given points (1, 3) and (0, -2).
Step 1: Calculate the slope (m):
The slope of a line passing through two points can be found using the formula:
m = (y2 - y1) / (x2 - x1)
Using the coordinates (1, 3) and (0, -2):
m = (-2 - 3) / (0 - 1)
m = (-5) / (-1)
m = 5
Step 2: Determine the y-intercept (b):
The y-intercept is the value of y when x = 0, using either of the given points:
Using the point (0, -2):
y = mx + b
-2 = 5(0) + b
-2 = b
Step 3: Write the equation in slope-intercept form:
We now have the slope (m = 5) and the y-intercept (b = -2). Plugging these values into the slope-intercept form equation gives us:
y = mx + b
y = 5x - 2
So, the equation of the line passing through the points (1, 3) and (0, -2) is y = 5x - 2 in slope-intercept form.
To derive the equation of the line in slope-intercept form, we need to find the slope and the y-intercept of the line using the given points (1, 3) and (0, -2).
The slope of a line can be found using the formula:
slope = (change in y) / (change in x)
Let's calculate the slope:
change in y = 3 - (-2) = 5
change in x = 1 - 0 = 1
slope = 5/1 = 5
Now that we have the slope, we can use the slope-intercept form of the equation of a line, which is:
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 and solve for b.
Let's use the point (1, 3):
3 = 5(1) + b
3 = 5 + b
Subtracting 5 from both sides:
3 - 5 = b
-2 = b
So, the y-intercept (b) is -2.
Now we can write the equation of the line using the slope and the y-intercept:
y = 5x - 2
Therefore, the equation of the line in slope-intercept form is y = 5x - 2.