Question

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

Answer 1

Answer:

y=5/4x-1

Step-by-step explanation:

-6-4/-4-4 = -10/-8 = 5/4 (slope)

y=5/4x+b

4=5/4(4)+b

b=-1

y=5/4x-1

Answer 2

Answer:

$y = \frac{5}{4} x -1$

Step-by-step explanation:

Find the slope of this line by using the slope formula: $\frac{y_2-y_1}{x_2-x_1}$. Substitute both given points into this formula.

$\frac{(-6)-(4)}{(-4)-(4)} \rightarrow\frac{-10}{-8} \rightarrow\frac{-5}{-4} =\frac{5}{4}$

The slope of the line is 5/4. Now this can be plugged into point-slope form since we have the point and the slope of the line.

Use any pair of given points, I'll be using (4,4).

Point-slope form: $y-y_1=m(x-x_1)$

Substitute 4 for $x_1$, 4 for $y_1$, and 5/4 for m.

$y-(4)=\frac{5}{4} (x-(4))$

Simplify this equation.

$y-4=\frac{5}{4} (x-4)\rightarrow y-4=\frac{5}{4} x-5\rightarrow y = \frac{5}{4} x -1$

The equation in slope-intercept form of the line is $y = \frac{5}{4} x -1$.