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

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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

**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

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.

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!

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