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

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:

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:

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)

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:

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

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

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)

d

step-by-step explanation:

hello and welcome!

so, when we see the words "proportional" along with a table, we need to know that we're looking numbers that divide by the same thing.

looking at this table, we simply have to do a trial and error, and divide to see which numbers have the same quotient. if you look at choice a & c, they both have equal quotients for three of the numbers, with one exception, so those can't be the answer. looking at b, there is no similarity, so that can't be it. then, we see d; if you divide all the numbers in the table, you'll see that they all divide by two, which is a proportional relationship, and our answer!

also, always remember that the x will always be the number that goes into y, and somewhere behind this table, is a formula. for this specific table, the formula would be:

since our x-value is being divided by two to get the y-value. and if they were to ask for more numbers in the series, this is the formula you would use to find them.