2points
identify an equation in slope-intercept form for the line parallel to y = 5x + 2
that passes through (-6, -1).

y = 2x + 11

Step-by-step explanation:

Slope-intercept form is written y = mx + b

"x" and "y" are points on the line.

"m" is the slope.

"b" is the y-intercept.

Parallel lines have the same slope.

A line parallel to y = 5x + 2 will have the slope 2. m = 2

To find "b", substitute the point (-6, -1) and m = 2 into slope-intercept form. Points are written (x, y), so x = -6 , y = -1

y = mx + b

-1 = (2)(-6) + b            Multiply 2 and -6

-1 = -12 + b            Isolate "b" by separating it from everything else

-1 + 12 = -12 + 12 + b           Add 12 to both sides

11 = b        Answer for b, the y-intercept

b = 11        Write variables on left side

Use the slope and y-intercept in slope-intercept form to write the equation.

y = 2x + 11

graph b

step-by-step explanation:

one solution- graph a (clear intercepting point.)

no solution- graph b (they're parallel, there will never be a point of interception.)

infinite solutions- graph c (all points intercept.)