Question

How do I solve this??? 15 points!

Answer 1

m = 7/2
y-4 = 7/2 (x-2)
y = 7/2x - 3

Answer 2

`\displaystyle y=(7)/(2)x-3`

Explanation:

We wan to determine the equation of a line that passes through the point (2, 4) and is parallel to:

`\displaystyle y=(7)/(2)x-5`

Since our new line is parallel to our equation, this means that the two lines have the same slope.

Therefore, the slope of our new line is also 7/2, the slope of the original.

Now, we can use the point-slope form:

`y-y_1=m(x-x_1)`

Where m is the slope and (x₁, y₁) is a point.

So, we will substitute 7/2 for m.

Let's let our point (2, 4) be (x₁, y₁). Hence:

`\displaystyle y-4=(7)/(2)(x-2)`

Solve for y. Distribute:

`\displaystyle y-4=(7)/(2)x-7`

Add 4 to both sides.Therefore, our equation is:

`\displaystyle y=(7)/(2)x-3`