write the equation of the line in slope-intercept form given the slope and the coordinates of the y-intercept
m = 3/7;(0, 8/3)
find an equation of the line described below. write the equation in slope-intercept form (solved for y) when possible.
through (6, 4) and (4, 6)
find an equation of the line described below. write the equation in slope-intercept form (solved for y) when possible.
With undefined slope, through (1/4, 5)
1. you are given the slope and the y-intercept.
You are asked to write the equation in slope intercept form
You know that form is y = mx + b
so just replace m and b
2. first find the slope:
slope = (6-4)/(4-6) = 2/-2 = -1
so you must have:
y = -x + b
sub in the point (4,6) , or (6,4) if you feel like it
with (4,6)
6 = -(4) + b
b = 10
your equation is y = -x + 10
3. All vertical lines have equation x = ???
look at your given point, the x value is 1/4
so your equation is y = 1/4
#3: x = 1/4
To find the equation of a line in slope-intercept form (y = mx + b), we need to know the slope (m) and the y-intercept (b).
Let's start with the first question:
1) Given the slope (m) = 3/7 and the y-intercept (0, 8/3):
The slope-intercept form of the line is y = mx + b, where m is the slope and b is the y-intercept.
So, we have m = 3/7 and b = 8/3.
Substituting these values into the equation, we get y = (3/7)x + 8/3.
Now let's move on to the second question:
2) Given the points (6, 4) and (4, 6):
First, we find the slope (m) using the formula: m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the two points.
Using the coordinates (6, 4) and (4, 6):
m = (6 - 4) / (4 - 6) = 2 / (-2) = -1.
Now we have the slope (m) = -1, and we can choose any of the two points to find the y-intercept (b).
Let's use the point (6, 4):
Substituting the values of m and the coordinates (x, y) of the point into the slope-intercept form, we get:
y = mx + b
4 = -1 * 6 + b
4 = -6 + b
b = 10.
So, the equation of the line is y = -x + 10.
Finally, let's solve the third question:
3) Given the undefined slope and the point (1/4, 5):
When the slope is undefined, it means the line is vertical, parallel to the y-axis. In this case, the equation of the line cannot be written in slope-intercept form.
However, we can still find the equation by noting that all points on the line have the same x-coordinate. In this case, x = 1/4.
So, the equation of the line is x = 1/4.