Question

The diagram shows a straight line ABCD.

A is the point (−260,480) D is the point (620,−180)
The line cuts the y-axis at B and the x-axis at C.

Answer 1

Difference:

x values

260 + 620 = 880

y values

480 + 180 = 660

Gradient = change in y/ change in x

Or

gradient = rise/run

= 660/880

= 3/4

= 0.75

We've got a negative slope - gradient must be negative

y = mx + c

y = - 0.75x + c

To find the y-intercept (c), which on the diagram is point B - you substitute one of the coordinates into the equation y = - 0.75x + c.

You use - point A or D - it don't matter which

I'll pick D - (620,−180)

y= -0.75x + c

-180 = - 0.75 x 620 + c

-180 = - 465 + c

+465

285= c

Thus, the equation is:

y = - 0.75x + 285

or

y = - 3/4x + 285

Where point B is (0,285) and C is (380,0)

To find:

B substitute x = 0 into the equation

(y= - 3/4 x 0 + 285)

C substitute y = 0 in the equation

0 = - 3/4x + 285

-285

- 285 = - 0.75x

÷ - 0.75

380 = x

( I converted 3/4 to 0.75 to make things clearer)

Hope this helps!

Answer 2

B (0, 285 ) , C (380, 0 )

Explanation:

the first step is to obtain the equation of the line in slope- intercept form

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

calculate m using the slope formula

m =
`(y_(2)-y_(1) )/(x_(2)-x_(1) )`

with (x₁, y₁ ) = A(- 260, 480 ) and (x₂, y₂ ) = D (620, - 180 )

m =
`(-180-480)/(620-(-260))` =
`(-660)/(620+260)` =
`(-660)/(880)` = -
`(66)/(88)` = - 0.75 , then

y = - 0.75x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equatio

using (620, - 180 ) , then

- 180 = - 465 + c ⇒ c = - 180 + 465 = 285

So y- intercept is B (0, 285 )

y = - 0.75x + 285 ← equation of line

to find the x- intercept , let y = 0 in the equation and solve for x

0 = - 0.75 + 285 ( subtract 285 from both sides )

- 285 = - 0.75x ( divide both sides by - 0.75 )

380 = x

x- intercept is C (380, 0 )