Question

What are the intercepts of the line?

What is the slope of the line?

Write a linear equation for the line?

Answer 1

Answer to Q1:

y-intercept is (0,5).

x-intercept is (4,0).

Explanation:

We have given a line on graph.

We have to find the intercepts of the line.

y-intercept is a point on line where the value of x is zero.

x-intercept is a point on line where the value of y is zero.

From graph , we observed that

when x = 0 ⇒ y = 5

when y = 0 ⇒ x = 4

Hence, y-intercept is (0,5).

x-intercept is (4,0).

Answer to Q2:

slope = m = -5/4

Explanation:

We have given a line on graph.

We have to find the slope of the line.

Using x and y-intercept, we can find the slope of line.

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

The formula to find slope is :

m = y₂-y₁ / x₂-x₁

Putting above values , we have

m = 0-5 / 4-0

m = -5/4 which is the answer.

Answer to Q3:

y = -5/4x+5

Explanation:

We have given a line on graph.

We have to find the equation of line.

y = mx+c is slope-intercept of equation where m is slope and c is y-intercept.

From above questions, slope = m = -5/4 and c = 5

Putting values in above equation, we have

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

y = -5/4x+5 which is the equation of line.

Answer 2

For this case we must find the equation of the line shown in the figure.

`y = mx + b`

Where:

m: It's the slope

b: It is the cutoff point with the y axis

`m = \frac {y2-y1} {x2-x1}`

We choose two points through which the straight line passes

(0,5)

(4,0)

`m = \frac {0-5} {4-0}\\m = - \frac {5} {4}`

Thus, the equation is:

`y = - \frac {5} {4} x + b`

We substitute any of the points to find "b".

`0 = - \frac {5} {4} (4) + b\\0 = -5 + b\\b = 5`

Thus, the cut point with the "y" axis is 5.

Answer:

Interceptions: (0,5) and (4,0)

Slope:
`- \frac {5} {4}`

Equation:
`y=-(5)/(4)x+5`