I need help with
write the equation of the line which contains the point (0,negavtive 3),
or written ars(0, -3)
and whose slope is 4.
if you want the equation in the form
y = mx + b
sub in -3 for y, 4 for m, and 0 for x
for
-3 = 4(0) + b
so b = -3
equation: y = 4x -3
We could have noticed that (0,-3) is the y-intercept and have directly into
y = 4x - 3
using the formula, y - (-3) = 4(x-0)
so y + 3 = 4x
y = 4x - 3
To find the equation of a line, we need a point on the line and its slope. In this case, the point given is (0, -3), and the slope is 4.
To write the equation in the form y = mx + b, we substitute the known values into the equation and solve for b:
Substitute -3 for y, 4 for m, and 0 for x:
-3 = 4(0) + b
Simplifying the equation gives us:
-3 = b
Therefore, b is equal to -3.
Plugging the values of m and b into the equation, we get:
y = 4x - 3
Alternatively, we can directly notice that (0, -3) is the y-intercept and write the equation as:
y = 4x - 3
Another way to derive the equation is by using the point-slope form. The point-slope form of a line is given by:
y - y1 = m(x - x1)
Substituting the given values, we have:
y - (-3) = 4(x - 0)
Simplifying gives us:
y + 3 = 4x
Finally, rearranging the equation gives us:
y = 4x - 3
So, the equation of the line containing the point (0, -3) and having a slope of 4 is y = 4x - 3.