Question

5) through (-2, -3) and (0,1)
Slope-Intercept:
Standard Form: ​

Answer 1

For this case we have that by definition, the equation of the line of the slope-intersection form is given by:

`y = mx + b`

Where:

m: It is the slope of the line

b: It is the cut point with the y axis

We have the following points:

`(x_ {1}, y_ {1}): (0,1)\\(x_ {2}, y_ {2}): (-2, -3)`

We find the slope:
`m = \frac {y_ {2} -y_ {1}} {x_ {2} -x_ {1}} = \frac {-3-1} {- 2-0} = \frac {-4} {- 2} = 2`

Thus, the equation is of the form:

`y = 2x + b`

We substitute a point and find b:

`1 = 2 (0) + b\\b = 1`

Finally, we have:

`y = 2x + 1`

On the other hand, the equation in the standard form is given by:

`ax + by = c`

So, according to the slope-intersection equation we have:

`2x-y = -1`

Answer:

`y=2x+1\\2x-y=-1`

Answer 2

Slope = 2

y-intercept = 1

x-intercept = -0.5

Standard Form ⇒ y - 2x = 1

Explanation:

write the equation of the line through (-2 , -3) and (0,1)

The general form of the line is y = mx + c

Where m is the slope and c is the y-intercept

The slope m = (y₂ - y₁)/(x₂ - x₁) = (1 - [-3])/(0 - [-2]) = 4/2 = 2

∴ y = 2x + c

By substitution with the point (0,1) to find c

1 = 2 *0 + c

c = 1

∴ y = 2x + 1

Or y - 2x = 1 ⇒Standard Form

Also,

See the attached figure which represents the graph of the line y - 2x = 1