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

Slope = 2

y-intercept = 1

x-intercept = -0.5

Standard Form ⇒ y - 2x = 1

Step-by-step 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

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

Where:

m: It is the slope of the line

b: It is the cut point with the y axis

We have the following points:

We find the slope:

Thus, the equation is of the form:

We substitute a point and find b:

Finally, we have:

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

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

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step-by-step explanation: