Question

Which line has the same slope as the lone passing through (-4,-1) and (-1,-7)

Answer 1

Answer:

1) 6x+3y=5    

Step-by-step explanation:

1) First, find the slope of the line passing through (-4, -1) and (-1, -7). Use the slope formula $m = \frac{y_2-y_1}{x_2-x_1}$. Substitute the x and y values of the two points into the formula and solve:

$m = \frac{(-7)-(-1)}{(-1)-(-4)} \\m = \frac{-7+1}{-1+4} \\m = \frac{-6}{3} \\m = -2$

So, the slope is -2.

2) Now, identify the slopes of the lines in the options. We already know the slope of $y = -\frac{1}{2} x-7$  is $-\frac{1}{2}$ since it is in slope-intercept form. y = -2 must have a slope of 0 since it's horizontal, and all equations with the format of y = a number are horizontal.

To find the slope of $6x + 3y = 5$, isolate y to put the equations into slope-intercept form ($y = mx + b$ format), and whatever the coefficient of the x-term is will be the slope.

$6x + 3y = 5\\3y = -6x+5\\y = -2x + \frac{5}{3}$.

So, the slope of the first option is -2. It matches the slope we calculated in the first step, so that must be the answer.