Write an equation of that passes through the points through the points (2,3 and (-2,5)

Question

Write an equation of that passes through the points through the points (2,3 and (-2,5)

Answer 1

First, let's visualize what this question is asking...

We want to know an equation that represents a line from the following two points on a graph: (2,3) and (-2,5).

When talking about a line, there are two properties that we care about: slope (relationship between x and y) and y-intercept (the value of y when x equals 0).

First, let's find the slope. Slope is the relationship between x and y. What happens each time you add an x? Slope between two points is determined by the change in y divided by change in x.

The change in y can be calculated by subtracting 3 from 5

5 - 3 = 2

The change in x can be calculated by subtracting 2 from -2.

-2 - 2 = -4

Divide the change in y by the change in x to find slope.

2 / -4 = -1/2

*You can think of -1/2 as "for every increase in x, y will change by -1/2 "

Now let's find the y intercept using a trick... we know that the y intercept of an equation is the y value when x equals 0, right? And now we know the slope: -1/2.

Slope = change in y / change in x

-1/2 = (3 - yint) / (2 - 0)

Above, we compared the known point (2,3) with the y-intercept (x equals zero).

Let's use some algebra to isolate our unknown (yint)

(-1/2)*(2 - 0) = 3 - yint

-1 - 3 = -yint

-1*(-4) = yint

yint = 4

GREAT! Now we know the two components of the line: the slope and y intercept.

Let's plug them into our equation y = slope (x) + yintercept

y = -1/2x + 4

Answer 2

Since we are given points, the quickest way would be to write the equation in point slope form.

Where (x1, y1) is any point on the line (hint: we are given two)

And m is the slope (hint: slope formula).

All we need is the slope. For that:

Now that we have the slope, all that's left is to plug it in to the point slope formula:

(x1 , y1) was randomly selected to be (2,3) although using (-2,5) would work just as well.

Answer 3

Hi, Ashlee.

Okay. So, so first you need to find the slope (m) of the line. To do this you take the Δy/Δx. So, for this line, you would calculate (5-3)/(-2-2)= -2/4 =-1/2.

Now, using the slope-intercept form of a line, you have y = mx+b. Since we know m = -1/2, we just need the y-intercept (b). To do this you can simply substitute one of the given points for the x and y in the equation. So, if we use point (2, 3) we have:

y = (-1/2) x + b.

3 = (-1/2)(2) + b.

3 = -1 + b

Now, solve for b by adding 1 to both sides...

3+1 = (-1+1) + b

4 = b

Now you can substitute b into the equation:

y = (-1/2)x + 4

Now, check the answer by substituting the other point (-2,5) into the equation....

5 = (-1/2)(-2) + 4

5 = 1+4

The equation is correct