Question

Write the slope-intercept form of the equation of each line

Answer 1

Answer: y= 3x-1

Step-by-step explanation:

Equation of a straight line:

y = mx + b ------(i)

Step by Step Solution:

Step 1: Calculating Slope (m).

m =

y2-y1

x2-x1

m =

2--1

1-0

m =

3

1

m = 3

Now putting value of m in equation (i)

y = 3x + b -----(ii)

Step 2: Calculating Y-intercept (b).

Lets choose the first point, (0,-1) for calculating y-intercept:

y = mx + b

-1 = 3(0) + b

-1 = 0 + b

-1 = b

b = -1

Answer 2

Answer:

y=3x-1

Step-by-step explanation:

Hi there!
We are given a line, and we want to find the equation of that line in slope intercept form

Slope-intercept form is given as y=mx+b, where m is the slope, and b is the y intercept

First, we need to find the slope of the line

The slope of the line can be calculated from 2 points with the equation $\frac{y_2-y_1}{x_2-x_1}$, where $(x_1, y_1)$ and $(x_2, y_2)$ are points

We can take any 2 points from the line to help us; for example, we can take (0,-1), and (1,2), which are both on the line

We can label the values of the points to avoid confusion while we calculate the slope:
$x_1=0\\y_1=-1\\x_2=1\\y_2=2$
Now let's plug these values into the formula to solve for the slope:

m=$\frac{y_2-y_1}{x_2-x_1}$

m=$\frac{2--1}{1-0}$

Simplify:

m=$\frac{2+1}{1-0}$

Add/subtract:

m=$\frac{3}{1}$

m=3

The slope of the line is 3
Remember that our equation is y=mx+b; we can plug 3 as m into the equation right now.

This is our equation so far:

y=3x+b

Now we need to find b
The y intercept (b) is the point in where the line intersects with the y axis; the value of x is 0 at that point

Since we have the graph given, we can find the value of the y intercept by finding the point that crosses (intersects) the y axis.

That point would be (0, -1)

The value of b is simply the value of y at this point; in this case, the value of b is -1

So plug -1 as b into the equation:

y=3x-1

Hope this helps!

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