Question

What is the equation of the line that passes through the points (−2, 1) and (1, 10)?

Answer 1

Answer:

Slope-Intercept form: y=3x+7

Standard form: 3x-y=-7

Point-slope form: y-1=3(x+2)

Step-by-step explanation:

Slope-Intercept form:

First, find the slope, using the formula: $m=\frac{y_{2}-y_{1} }{x_{2}-x_{1} }$

Our x₁ and y₁ will be the point (-2,1) and our x₂ and y₂ wwill be the point (1,10).

So let's write those in our equation to find slope:

$m=\frac{10-1}{1-(-2)}=\frac{9}{3}=3$

Therefore, our slope is 3.

Now let's write our linear equation with what we have already in slope-intercept form:

y=3x+b

Well, we still need to find the y-intercept, or "b".

Plug in one of your points for the x and y values of the equation.  We'll use the point (-2,1)

$y=3x+b\\1=3(-2)+b\\1=-6+b\\1+6=-6+6+b\\7=b$

This means our y-intercept is 7.  Now we can write our equation in slope-intercept form completely:

y=3x+7

Standard form:

Now, let's find this equation is standard form.

Take your equation in slope-intercept form and write it out again:

$y=3x+7$

Now, standard form of a linear equation is ax+by=c, so subtract 3x from both sides:

$y-3x=3x-3x+7\\-3x+y=7$

The "a" coefficient in standard form cannot be negative, so divide the entire equation by -1:

$\frac{-3x+y}{-1}=\frac{7}{-1}\\3x-y=-7$

Therefore, your equation in standad form is:

3x-y=-7

Point-Slope form:

The formula for point-slope form is y-y₁=m(x-x₁).  We already know that our x₁ and y₁ is the point (-2,1) and we know that our slope, m, is 3, so we just have to plug then in where the fit in the equation.

x₁ is -2 and y₁ is 1 and m is 3, so:

y-1=3(x-(-2)) or y-1=3(x+2)

That means our equation in point-slope form is:

y-1=3(x+2)