Recall that the form of the line y = m x + b
is what is called the slope-intercept form because the slope "m"is shown explicitly in it, and the y-intercept value is shown as the "b"
In our case, we are asked to find the equation of the line in slope-intercept form for a slope m= -1/3 and also make sure that the line goes through the point (6, -4) on the plane
So we work directly from the general form given above:
y = m x + b
knowing that m = - 1/3
Then we have:
y = -1/3 x + b
now, to find "b"we use the information about the point (6 , -4) the line goes through, replacing these x and y values in the equation, and solving for "b":
Notice that x = 6 and y = -4 in that point
- 4 = -1/3 (6) + b
- 4 = - 6/3 + b
- 4 = - 2 + b
add 2 to both sides
- 4 + 2 = b
- 2 = b
Then the equation for this line reads:
y = - 1/3 x - 2
which agrees with the very first answer in the list of possible options.
