write an equation in standard form for the line that passes through the given points. (6,0) and (0,8)
in standard form
4x+3y = 24
slope = m = (8 - 0) / (0 - 6) = - 4/3
so
y = -(4/3) x + b
put a point in like (0,8)
8 = 0 + B
b = 8
so
y= -(4/3) x + 8
or
3 y = -4 x + 24
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check, put in (6,0)
3(0) = -(4/3) (6) + 8 ???
0 = -8 + 8 sure enough
Why did the line go to the circus? Because it wanted to pass through the given points and perform some high-flying comedy! Now, let's get down to business and write the equation in standard form.
First, let's find the slope (m) of the line using the formula: m = (y2 - y1) / (x2 - x1)
Using the points (6,0) and (0,8):
m = (0 - 8) / (6 - 0)
m = -8 / 6
m = -4 / 3
Now that we have the slope, we can use the point-slope form of a line (y - y1) = m(x - x1) and plug in one of the points (let's choose (6,0)):
(y - 0) = (-4/3)(x - 6)
y = -4/3x + 8
Finally, let's rewrite the equation in standard form (Ax + By = C):
Multiply everything by 3 to get rid of fractions:
3y = -4x + 24
Rearranging:
4x + 3y = 24
So, the equation in standard form for the line passing through (6,0) and (0,8) is 4x + 3y = 24. Now that's a mathematical spectacle!
To find the equation in standard form for the line passing through the points (6,0) and (0,8), we can follow these steps:
Step 1: Use the formula for the slope (gradient) of a line:
slope (m) = (change in y) / (change in x)
slope (m) = (y2 - y1) / (x2 - x1)
Let's use the points (6,0) and (0,8):
m = (0 - 8) / (6 - 0)
m = -8 / 6
m = -4 / 3
Step 2: Next, we use the slope-intercept form of the equation for a line:
y = mx + b
We substitute the value for m = -4/3 and use one of the two given points to find the value of b.
Let's use the point (6,0):
0 = (-4/3) * 6 + b
b = 8
Therefore, the equation of the line in slope-intercept form is y = (-4/3)x + 8.
Step 3: Finally, we'll convert the equation to standard form: Ax + By = C.
Multiply the equation by 3 to eliminate the fraction:
3y = -4x + 24
Rearrange the equation:
4x + 3y = 24
Thus, the equation of the line passing through the points (6,0) and (0,8) in standard form is 4x + 3y = 24.
To write an equation in standard form for a line passing through two given points, we can follow these steps:
Step 1: Find the slope (m) of the line using the formula:
m = (y2 - y1) / (x2 - x1)
Given the points (6,0) and (0,8), we can substitute the values into the formula:
m = (0 - 8) / (6 - 0)
m = -8 / 6
m = -4/3
Step 2: Use the slope-intercept form of a line (y = mx + b) and substitute one of the points to solve for the y-intercept (b).
Using the point (6,0), substitute x = 6 and y = 0 into the equation:
0 = (-4/3)(6) + b
0 = -8 + b
b = 8
Step 3: Substitute the slope (m) and y-intercept (b) into the equation y = mx + b to get the final equation.
Using the values we found, the equation becomes:
y = (-4/3)x + 8
To convert the equation into standard form, we need to multiply throughout by 3 to eliminate the fraction:
3y = -4x + 24
Finally, rearrange the equation so that the variables are on the left side and the constant is on the right side:
4x + 3y = 24
Therefore, the equation in standard form for the line passing through the points (6,0) and (0,8) is:
4x + 3y = 24