Question

Need Answer Immediately!!!!!

Answer 1

y =
`(-5)/(4)`x + 3

Explanation:

As shown in the graph, the line is a straight line. Therefore, the general equation of a straight line can be employed to derive the equation of the line.

The general equation of a straight line is given by:

y = mx + c or -------------(i)

y - y₁ = m(x - x₁) -----------------(ii)

Where;

y₁ is the value of a point on the y-axis

x₁ is the value of the same point on the x-axis

m is the slope of the line

c is the y-intercept of the line.

Equation (i) is the slope-intercept form of a line

Steps:

(i) Pick any two points (x₁, y₁) and (x₂, y₂) on the line.

In this case, let;

(x₁, y₁) = (0, 3)

(x₂, y₂) = (4, -2)

(ii) With the chosen points, calculate the slope m given by;

m =
`(y_2 - y_1)/(x_2-x_1)`

m =
`(-2-3)/(4-0)`

m =
`(-5)/(4)`

(iii) Substitute the first point (x₁, y₁) = (0, 3) and m =
`(-5)/(4)` into equation (ii) as follows;

y - 3 =
`(-5)/(4)`(x - 0)

(iv) Solve for y from (iii)

y - 3 =
`(-5)/(4)`x

y =
`(-5)/(4)`x + 3 [This is the slope intercept form of the line]

Where the slope is
`(-5)/(4)` and the intercept is 3