Question

A line passes through the point , ( − 6, 1) and has a slope of − 4/3 .

Answer 1

A line with a slope of -4/3 passes through the point (-6, 1) can be represented by the equation y = -4/3x - 7.

Step-by-step explanation:

A line with a slope of -4/3 passes through the point (-6, 1).

To find the equation of the line, we can use the point-slope form of a linear equation: y - y1 = m(x - x1), where (x1, y1) is the given point and m is the slope.

Substituting the values into the equation, we get y - 1 = -4/3(x - (-6)).

Simplifying, we have y - 1 = -4/3(x + 6).

Expanding, y - 1 = -4/3x - 8.

Moving the constant term to the other side, we get y = -4/3x - 7.

Answer 2

Slope-intercept form:

y = mx + b

"m" is the slope, "b" is the y-intercept (the y value when x = 0 or (0,y))

Since you know m = -4/3, plug it into the equation

y = -4/3x + b

To find "b", plug in the point into the equation

y = -4/3x + b

1 = -4/3(-6) + b

1 = 24/3 + b

1 = 8 + b

-7 = b

y = -4/3x - 7