Question

What is the equation of the line that passes through (-2, 4) and (2, 7)?

Answer 1

Answer:

$y=\frac{3}{4}x+\frac{11}{2}$

Step-by-step explanation:

Hi there!

We want to find the equation of the line that passes through (-2, 4) and (2, 7).

The most common way to write the equation of the line is in slope-intercept form, which is y=mx+b, where m is the slope and b is the y intercept.

First, let's find the slope of the line.

The slope, calculated from two points is given as the formula $\frac{y_2-y_1}{x_2-x_1}$, where $(x_1, y_1)$ and $(x_2, y_2)$ are points.

We have two points, which is needed to find the slope, but let's label their values to avoid confusion.

$x_1=-2\\y_1=4\\x_2=2\\y_2=7$

Now substitute those values into the formula.

m=$\frac{y_2-y_1}{x_2-x_1}$

m=$\frac{7-4}{2--2}$

Simplify

m=$\frac{7-4}{2+2}$

m=$\frac{3}{4}$

So the slope of the line is $\frac{3}{4}$.

Substitute that value as m in y=mx+b

y=$\frac{3}{4}x+b$

Now we need to find b

As the equation passes through both (-2, 4) and (2, 7), we can substitute the values of either one of them in the equation to solve for b

Taking (-2, 4) for example,

Substitute -2 as x and 4 as y:

4=$\frac{3}{4}(-2)+b$

Multiply

4=$-\frac{3}{2}$+b

Add -3/2 to both sides

$\frac{11}{2} = b$

Substitute that value into the equation

y=$\frac{3}{4}x+\frac{11}{2}$

Hope this helps!