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 [tex]m = \frac{y_2-y_1}{x_2-x_1}[/tex]. Substitute the x and y values of the two points into the formula and solve:
[tex]m = \frac{(-7)-(-1)}{(-1)-(-4)} \\m = \frac{-7+1}{-1+4} \\m = \frac{-6}{3} \\m = -2[/tex]
So, the slope is -2.
2) Now, identify the slopes of the lines in the options. We already know the slope of [tex]y = -\frac{1}{2} x-7[/tex] is [tex]-\frac{1}{2}[/tex] 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 [tex]6x + 3y = 5[/tex], isolate y to put the equations into slope-intercept form ([tex]y = mx + b[/tex] format), and whatever the coefficient of the x-term is will be the slope.
[tex]6x + 3y = 5\\3y = -6x+5\\y = -2x + \frac{5}{3}[/tex].
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.
