Question

What are the intercepts of the line?

Answer 1

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: $y=-\frac{5}{4}x+5$

Answer 2

Answer to Q1:

y-intercept is (0,5).

x-intercept is (4,0).

Step-by-step 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

Step-by-step 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

Step-by-step 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.