graphing equations practice
use the image to answer the question
(0,-2), (3,0)
write the equation of the line in slope intercept form
To write the equation of a line in slope-intercept form (y = mx + b), you need to determine the values of the slope (m) and the y-intercept (b).
Given the two points (0, -2) and (3, 0), we can use the slope formula:
m = (y2 - y1) / (x2 - x1)
Let's substitute the coordinates into the formula:
m = (0 - (-2)) / (3 - 0)
m = 2 / 3
Now that we have the slope (m), we can substitute the values of one of the points into the slope-intercept form to find the y-intercept (b).
Choosing the point (3, 0):
0 = (2/3)(3) + b
0 = 2 + b
Solving for b:
b = -2
Now we have both the slope (m = 2/3) and the y-intercept (b = -2), so we can write the equation of the line in slope-intercept form:
y = (2/3)x - 2
To write the equation of a line in slope-intercept form (y = mx + b), we need the slope (m) and the y-intercept (b).
First, let's find the slope (m) using the given points (0, -2) and (3, 0):
m = (y2 - y1)/(x2 - x1)
m = (0 - (-2))/(3 - 0)
m = 2/3
Now, let's substitute one of the given points (0, -2) and the slope (2/3) into the slope-intercept form (y = mx + b) to find the value of the y-intercept (b):
-2 = (2/3)(0) + b
-2 = 0 + b
b = -2
Therefore, the equation of the line in slope-intercept form (y = mx + b) is:
y = (2/3)x - 2
To find the equation of the line in slope-intercept form, we need to determine the slope of the line and the y-intercept.
Given the points (0, -2) and (3, 0), we can first find the slope using the formula:
slope (m) = (change in y) / (change in x)
m = (0 - (-2)) / (3 - 0)
= 2 / 3
Now that we have the slope, we can use the point-slope form of the equation of a line:
y - y1 = m(x - x1)
Let's choose one of the given points, say (3, 0), and substitute its coordinates into the equation:
y - 0 = (2/3)(x - 3)
Simplifying:
y = (2/3)(x - 3)
Thus, the equation of the line in slope-intercept form is y = (2/3)(x - 3).