find the equation of the line with a slope of 4 and passing through (0 3)
y-3 = 4(x-0)
(0, 3), m = 4.
Y = mx + b.
3 = 4*0 + b,
b = 3.
Eq: Y = 4x + 3.
To find the equation of a line with a given slope and passing through a given point, you can use the point-slope form of a linear equation. The point-slope form is given by:
y - y1 = m(x - x1)
Where:
- m is the slope of the line, and
- (x1, y1) are the coordinates of the given point.
So, in this case, the slope (m) is 4, and the point (0,3) is given. Let's substitute these values into the point-slope form:
y - 3 = 4(x - 0)
Simplifying:
y - 3 = 4x
Now, to obtain the equation in more familiar slope-intercept form (y = mx + b), you can rearrange the equation by isolating y:
y = 4x + 3
Therefore, the equation of the line with a slope of 4 and passing through (0,3) is y = 4x + 3.