What is an equation of the line that passes through the points (3,6) and (1,−2)?

Slope-intercept form, which is y=mx+b, where m is the slope and b is the y intercept
Standard form, which is ax+by=c, where a, b, and c are integer coefficients but a and b cannot be equal to 0, and a cannot be negative
Slope-point form, which is [tex]y-y_1=m(x-x_1)[/tex], where m is the slope and [tex](x_1, y_1)[/tex] is a point

The most common way is slope-intercept form, so let's write the equation of the line this way

First, we need to find the slope

The slope (m) can be found using the formula [tex]\frac{y_2-y_1}{x_2-x_1}[/tex], where [tex](x_1, y_1)[/tex] & [tex](x_2, y_2)[/tex] are points

Before we calculate, let's label the values of the points.

[tex]x_1=3\\y_1=6\\x_2=1\\y_2=-2[/tex]

Now substitute into the formula

m=[tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

m=[tex]\frac{-2-6}{1-3}[/tex]

Subtract

m=[tex]\frac{-8}{-2}[/tex]

Divide

m= 4

The slope of the line is 4

Substitute 4 as m in y=mx+b:

y = 4x + b

Now to find b

Since the equation passes through both (3,6) and (1, -2), we can use either point to help solve for b.

Taking (3,6) for example:

Substitute 3 as x and 6 as y.

6 = 4(3) + b

Multiply

6 = 12 + b

Subtract 12 from both sides

-6 = b

Substitute -6 as b into the equation

y = 4x - 6

Hope this helps!

Topic: finding the equation of the line

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