Question

Write the equation of a line that passes through the points (0, -2) and (4, -5). Answer MUST be in standard form: Ax + By = C.

Answer 1

Steps:

• Slope-Intercept Form: y = mx + b (m = slope, b = y-intercept)
• Standard Form: Ax + By = C (A, B, & C are integers and A must be non-negative)
• Slope Formula: $\frac{y_2-y_1}{x_2-x_1}$ where (x₁,y₁) and (x₂,y₂) are coordinates.

So for this, I will be putting the equation into slope-intercept form then rearranging it into standard form. Firstly, we need to solve for the slope. To do this, take the 2 coordinates given to us and solve as such:

$\frac{-5-(-2)}{4-0}=-\frac{3}{4}$

Now, one of the coordinates given to us is (0,-2), which is the y-intercept. With all this info, our slope-intercept equation is $y=-\frac{3}{4}x-2$ . From here we can solve for the standard form.

Firstly, add 3/4x onto both sides of the equation:

$\frac{3}{4}x+y=-2$

Now, it may appear that we are finished. However, 3/4 is not an integer (Integers are whole numbers). To make it an integer, we need to multiply both sides by 4:

$3x+4y=-8$

Answer:

In short, the standard form of this equation is 3x + 4y = -8.

Answer 2

The slope-intercept form:

$y=mx+b$

m - slope

b - y-intercept → (0, b).

We have the points (4, -5) and (0, -2) → y-intercept → b = -2.

The formula of a slope:

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

Substitute:

$m=\dfrac{-2-(-5)}{0-4}=\dfrac{-2+5}{-4}=\dfrac{3}{-4}=-\dfrac{3}{4}$

Therefore we have the equation of a line

$y=-\dfrac{3}{4}x-2$

Convert to the standard form: $Ax+By=C$

$y=-\dfrac{3}{4}x-2\qquad\text{multiply both sides by 4}\\\\4y=-3x-8\qquad\text{add 3x to both sides}\\\\\boxed{3x+4y=-8}$