Question

What is an equation of the line that passes through the points (−3,−4) and (-4, -6)

Answer 1

Answer:

• $\Large\boxed{\sf{y=2x+2}}$

Step-by-step explanation:

Use the slope formula.

SLOPE FORMULA:

$\Rightarrow: \sf{\dfrac{y_2-y_1}{x_2-x_1}}$

• y2=(-6)
• y1=(-4)
• x2=(-4)
• y1=(-3)

$:\Longrightarrow \sf{\dfrac{-6-\left(-4\right)}{-4-\left(-3\right)}}$

Solve.

$\sf{\dfrac{-6-\left(-4\right)}{-4-\left(-3\right)}=\dfrac{-6+4}{-4+3}=\dfrac{-2}{-1}=2}$

The slope is 2.

Use the slope-intercept form.

SLOPE-INTERCEPT FORM:

$\sf{y=mx+b}$

• X=slope
• B=y-intercept.
• The y-intercept is 2.

y=2x+2

• Therefore, the final answer is y=2x+2.

I hope this helps, let me know if you have any questions.

Answer 2

$\text{Given that,}\\\\(x_1,y_1) =(-3,-4)~~ \text{and}~~ (x_2,y_2) = (-4,-6)\\\\\text{Slope,}~m = \dfrac{y_2 -y_1}{x_2 -x_1} = \dfrac{-6+4}{-4+3} = \dfrac{-2}{-1} =2\\ \\\text{Equation of line,}\\\\~~~~~y-y_1 = m(x-x_1)\\\\\implies y+4=2(x+3)\\\\\implies y =2x+6-4\\ \\\implies y= 2x+2$