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Allisa [31]
3 years ago
7

The point-slope form of the equation of a line that passes through points (8, 4) and (0, 2) is y – 4 = (x – 8). What is the slop

e-intercept form of the equation for this line?
Mathematics
1 answer:
Elenna [48]3 years ago
8 0
The slope-intercept formula can be written as follows:

y = mx + b

The variable "m" represents the slope of the line, while "b" represents the y-intercept. We'll start with the y-intercept.

We know that the y-intercept can be defined as the value of "y" when "x" is equal to zero. To do this, we will need to find point (0,y). The original problem gives us two points, one of which is (0,2). Because "x" is equal to zero, we know that the y-intercept is 2. Substitute this value into the slope-intercept formula:

y = mx + 2

Now we need to find the slope. Slope can be defined as the "rise" of the line over the "run" of the line. In other words, calculate the change in y-value over the change in x-value. To do this, we will use the "x" and "y" values of the two points given in the problem.

Starting with the y-values (rise), we have 2 and 4. The difference between these two values is 2. Moving on to the x-values (run), we have 0 and 8. The difference between these two values is 8. Now put rise over run and substitute this value into the slope-intercept formula:

y = (2/8)x + 2

Now simplify the right side of the equation:

y = (1/4)x + 2

We now have a complete slope-intercept formula of the line.

I hope this helps!
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What is the equation of the line that passes through (4, 2) and is parallel to 3x – 2y = -6?
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Answer:

y = \frac{3}{2} x - 4

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Rearrange 3x - 2y = - 6 into this form

Subtract 3x from both sides

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y = \frac{3}{2} x + 3 ← in slope- intercept form

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• Parallel lines have equal slopes, hence

y = \frac{3}{2} x + c ← partial equation of parallel line

To find c substitute (4, 2) into the partial equation

2 = 6 + c ⇒ c = 2 - 6 = - 4

y = \frac{3}{2} x - 4 ← equation of parallel line

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