Question

What is an equation of the line that passes through the point (4,−6) and has a slope of -3 ?

1) y=−3x+6
(2) y=−3x−6
3) y=−3x+10
4) y=−3x+14

Answer 1

The correct equation of the line passing through the point (4, -6) with a slope of -3 is y = -3x + 6, which corresponds to option (1).

Step-by-step explanation:

To find the equation of the line that passes through the point (4, -6) and has a slope of -3, we use the point-slope form of the equation of a straight line, which is y - y1 = m(x - x1), where m is the slope and (x1, y1) is the point the line passes through. Plugging in our values, we get:

y - (-6) = -3(x - 4)

Simplifying, we get:

y + 6 = -3x + 12

Finally, we subtract 6 from both sides to get the equation of the line in slope-intercept form:

y = -3x + 6

The correct equation from the options given is therefore (1) y = -3x + 6.

Answer 2

y = -3x + 6.

Step-by-step explanation:

To isolate y, we can subtract 6 from both sides, resulting in y = -3x + 6. Therefore, the equation of the line that passes through the point (4,-6) and has a slope of -3 is y = -3x + 6.