Question

A line has a slope of 3 and passes through the point (2,31). Write the equation of the line in slope-intercept form

Answer 1

y=3x+25

Explanation:

So to find the slope-intercept we need to find the slope and the y intercept. we already know the slope so to find the y intercept you subtract 2 from the x coordinate and 6 from the y, because the slope is 3. So the answer is y=3x+23

Answer 2

y=3x+25

Explanation:

We are given a point and the slope, so let's use the slope-intercept equation.

`y-y_(1)=m(x-x_(1))`

where m is the slope and (x₁, y₁) is the point given. The slope is 3 and the point is (2,31). Therefore,

`m= 3 \\x_(1)=2\\y_(1)=31`

Substitute the values into the equation.

`y-31=3(x-2)`

We want the equation in slope intercept form: y=mx+b. We must isolate y on the left side of the equation.

First, distribute the 3. Multiply each term inside the parentheses by 3.

`y-31= (3*x)+(3*-2)`

`y-31=(3x)+(-6)`

`y-31=3x-6`

Next, add 31 to both sides of the equation.

`y-31+31=3x-6+31`

`y=3x-6+31`

`y=3x+25`

This equation is in slope intercept form, so our final answer is:

y= 3x+25 (slope⇒3 , y-intercept ⇒25)