Determine the equation of the following (a) Gradient -1/2 and intercept 5 on the vertical axis (B) Gradient 4 passing through (-3,-2)?

(a) The equation of a line can be written in the form y = mx + c, where m is the gradient and c is the y-intercept.

Given that the gradient is -1/2 and the intercept on the vertical axis is 5, we have m = -1/2 and c = 5.

Therefore, the equation of the line is y = -1/2x + 5.

(b) Given that the gradient is 4 and the line passes through the point (-3, -2), we can use the point-slope form of the equation of a line:

y - y1 = m(x - x1)

Substitute the values of the point (-3, -2) and the gradient 4 into the equation:

y - (-2) = 4(x - (-3))
y + 2 = 4(x + 3)
y + 2 = 4x + 12
y = 4x + 10

Therefore, the equation of the line is y = 4x + 10.

(a) Gradient -1/2 and intercept 5 on the vertical axis

The equation of a straight line is given by y = mx + c, where m is the gradient and c is the y-intercept.

Given the gradient is -1/2 and the y-intercept is 5, we have the equation:

y = (-1/2)x + 5

(b) Gradient 4 passing through (-3,-2)?

If the straight line passes through the point (-3,-2), then the coordinates of the point satisfy the equation of the line. Substituting x = -3 and y = -2 into the equation y = mx + c, we get:

-2 = 4(-3) + c

-2 = -12 + c

c = 10

Therefore, the equation of the straight line is:

y = 4x + 10