``slope 3, passes through (-2, 4)`` Write an equation in slope-intercept form that satisfies each set of conditions.

Textbook Question

Chapter 2, 2.6 - Problem 56 - Glencoe Algebra 2 (1st Edition, McGraw-Hill Education).
See all solutions for this textbook.

5 Answers | Add Yours

mathace's profile pic

mathace | (Level 3) Assistant Educator

Posted on

The slope intercept-form of an equation of a line is y=mx+b

Given that the slope is 3 and a point on the line is P(-2, 4), then

m=3 and from the point (-2, 4), x=-2 and y=4.

Substitute the m, x, and y into the slope intercept form

y=mx+b.

4=3(-2)+b   Now solve for b.

4=-6+b

4+6=b

10=b

Now you know b=10 and you already know the slope m=3. Substitute these values into y=mx+b. When you do you will get y=3x+10. This is your answer in slope intercept form.

hkj1385's profile pic

hkj1385 | (Level 1) Assistant Educator

Posted on

Equation of the line having slope 'm' & passing through a point (a,b) is :-

y - b = m(x-a)

The standard for of representing a line in slope-intercept form is :-

y = mx + b ; where m = slope of the line & 'b' = y-intercept

Now, the line passes through the point (-2,4) & has slope 3

Thus,  equation of the line is :-

y - (4) = 3*(x-(-2))

or, y - 4 = 3x + 6

or, y = 3x + 10 = slope-intercept representation of the line

sschall's profile pic

sschall | Middle School Teacher | (Level 1) Adjunct Educator

Posted on

If we know that the slope of our line is 3 and the point that it is passing through is (-2,4), then we can use slope-intercept form to solve it. The formula y=mx+b.  In this formula the m represents the slope, the x and y represent the coordinates of the point, and the b represents the y-intercept (where it crosses the y axis of the graph).  Let's begin by plugging in what we know:

4=3(-2)+b   Our first step is to solve for b so that we can find our intercept.

4= -6+b

+6   +6

-----------

10=b

Once we know what our y-intercept (b) is, we can the go back to our original equation and rewrite it so that it is in slope-intercept form.  In slope-intercept form the values of x and y are left out so that other points along the line can be determined.  Therefore our solution will be y=3x+10

iamtall14's profile pic

iamtall14 | (Level 2) eNoter

Posted on

Hi!

The slope (m) as given in the question is 3 which means m=3.

You are given points (-2,4) through which the line passes.

As you may recall, the slope intercept form is y=m*x+b, where:

m=slope = 3 

x=x point = -2

y=y point = 4

b=constant = ?(you have to figure it out!)

  • So you just plug in the values for the variables and solve for b

4 = 3*(-2)+b

4 = -6+b

b= 10

Once you have solved for b, you simply plug it in the equation y=m*x+b

So, y = 3x + 10 is the equation that has a slope of 3 and passes through (-2,4) 

Note: For the final equation, you only need to plug in the value of m and b. ( as seen above) For y and x you just write y and x , not the numerical value.

Hope this helps!

Educator Approved

Educator Approved
kspcr111's profile picture

kspcr111 | In Training Educator

Posted on

Given `m= 3` and the line passes through the point `(x_1,y_1)=(-2,4)`

the slope-intercept form is `y= mx+b`

we can find the equation of the line as 

`(y-y_1)= m(x-x_1)`

=>` (y - 4)= 3(x-(-2))`

=> `(y-4)= 3(x+2)`

=> `y-4= 3x+6`

=> `y = 3x+10`

is the slope-intercept form 

We’ve answered 318,911 questions. We can answer yours, too.

Ask a question