Question

Write the slope-intercept form (y=mx+b) of the equation of the line through the given slope.​

Answer 1

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

Explanation:

The equation of a line in slope- intercept form is

y = mx + b ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (- 5, 0) and (x₂, y₂ ) = (0, 4)

m =
`(4-0)/(0+5)` =
`(4)/(5)`

Note the line crosses the y- axis at (0, 4) ⇒ b = 4

y =
`(4)/(5)` x + 4 ← equation of line

Answer 2

Answer: y = 4x/5 + 4

Explanation:

The equation of a straight line can be represented in the slope-intercept form, y = mx + c

Where c = intercept

Slope, m =change in value of y on the vertical axis / change in value of x on the horizontal axis

change in the value of y = y2 - y1

Change in value of x = x2 -x1

y2 = final value of y

y 1 = initial value of y

x2 = final value of x

x1 = initial value of x

The line passes through (- 5, 0) and (0, 4),

y2 = 4

y1 = 0

x2 = 0

x1 = - 5

Slope, m = (4 - 0)/(0 - - 5) = 4/5

To determine the intercept, we would substitute x = 0, y = 4 and

m = 4/5 into y = mx + c. It becomes

4 = 4/5 × 0 + c

c = 4

The equation becomes

y = 4x/5 + 4