Line CD passes through points C(3, -5) And D(6, 0). What is the equation of line CD in standard form?
2 answers:
Answer:
5x - 3y = 30
Step-by-step explanation:
First we find the slope of the line using the formula
Using our points, we have
m = (-5-0)/(3-6) = -5/(-3) = 5/3
Next we write the equation using point-slope form. Using the slope of 5/3 and the second point, we have
y-0 = 5/3(x-6)
y = 5/3(x-6)
Using the distributive property, we have
y = 5/3(x)-5/3(6)
y = 5/3(x)-5/3(6/1)
y = 5/3(x)-30/3
y = 5/3x - 10
We cannot have fractions in standard form. To deal with this, we will multiply all 3 terms by 3:
3y = 5/3x(3) - 10(3)
3y = 5x - 30
We want x and y on the same side; subtract 5x from each side:
3y-5x = 5x-30-5x
-5x+3y = -30
We want x to be positive; multiply all 3 terms by -1:
5x-3y = 30
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Answer:
y = 4x + 14
Step-by-step explanation:
slope-intercept form: y = mx + b
Slope formula:
To write the equation in y = mx + b form, we need to find the slope(m) and the y-intercept(b) of the equation.
To find the slope, take two points from the table(in this example I'll use points (0, 14) and (1, 18)) and input them into the slope formula:
Simplify:
18 - 14 = 4
1 - 0 = 1
The slope is 4.
To find the y-intercept, input the values of the slope and one point(in this example I'll use point (1, 18)) into the equation format and solve for b:
y = mx + b
18 = 4(1) + b
18 = 4 + b
14 = b
The y-intercept is 14.
Now that we know the slope and the y-intercept, we can write the equation:
y = 4x + 14