Find an equation of the line described below. Write the equation in​ slope-inter

slaggingV

slaggingV

Answered question

2021-09-20

Find an equation of the line described below. Write the equation in​ slope-intercept form​ (solved for​ y), when possible. 
Through (8​,4​) and (4​,8​) 
What is the equation of the​ line?

Answer & Explanation

Elberte

Elberte

Skilled2021-09-21Added 95 answers

(x1,y1)=(8,4) 
(x2,y2)=(4,8) 
m=y2y1x2x1 =8448 =44 =-1 
The equation of the line passing through (x1,y1)(x1,y2) with slope m is 
yy1=m(xx1) 
y4=1(x8)  
y=x+8+4 
y=x+12

madeleinejames20

madeleinejames20

Skilled2023-06-11Added 165 answers

Result:
y=x+12
Solution:
y=mx+b
where m represents the slope of the line and b represents the y-intercept.
First, let's calculate the slope m using the given points (8,4) and (4,8). The slope is given by:
m=y2y1x2x1
Substituting the coordinates (x1,y1)=(8,4) and (x2,y2)=(4,8), we have:
m=8448
Simplifying this expression, we get:
m=44=1
Now that we have the slope, we can substitute it along with one of the given points into the slope-intercept form equation y=mx+b to solve for b. Let's use the point (8,4):
4=1·8+b
Simplifying this equation, we find:
4=8+b
Adding 8 to both sides, we get:
b=12
Therefore, the equation of the line in slope-intercept form is:
y=x+12
Eliza Beth13

Eliza Beth13

Skilled2023-06-11Added 130 answers

Step 1: Find the slope (m) of the line using the formula:
m=y2y1x2x1
where (x1,y1) and (x2,y2) are the coordinates of the two points.
Substituting the given points:
m=8448
m=44
m=1
Step 2: Use the slope-intercept form equation y=mx+b and substitute one of the points to find the y-intercept (b).
Using the point (8, 4):
4=1·8+b
4=8+b
b=12
Step 3: Write the equation of the line using the found slope (m=1) and y-intercept (b=12):
y=x+12
Therefore, the equation of the line passing through (8, 4) and (4, 8) in slope-intercept form is:
y=x+12
Nick Camelot

Nick Camelot

Skilled2023-06-11Added 164 answers

To find the equation of a line passing through the points (8, 4) and (4, 8), we can use the slope-intercept form of a linear equation:
y=mx+b
where m is the slope of the line and b is the y-intercept.
First, let's find the slope (m) using the formula:
m=y2y1x2x1
where (x1,y1) and (x2,y2) are the coordinates of the two given points.
Using the given points (8, 4) and (4, 8):
m=8448=44=1
Now that we have the slope, we can substitute it into the slope-intercept form equation along with the coordinates of one of the points to find the y-intercept (b).
Using the point (8, 4):
4=1·8+b
Simplifying:
4=8+b
b=48
b=4
Therefore, the y-intercept is 4.
Now we can write the equation of the line in slope-intercept form:
y=1x4
Simplifying:
y=x4
Hence, the equation of the line passing through the points (8, 4) and (4, 8) in slope-intercept form is y=x4.

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