Question

7. How could the function y=3x2+4 be plotted on a Cartesian graph to produce a straight line? What would be the numerical values of the slope and intercept of the line?

Answer 1

Given that,

The function is

$y=3x^2+4$

We know that,

The general equation of slope and intercept is

$y=mx+b$

Where, m = slope

b = intercept of the line

We need to find the slope and intercept

Using given function

$y=3x^2+4$

Suppose, $x^2=X$

Put the the value in the equation

$y = 3X+4$.....(I)

Now, comparing from general equation

$y=mx+b$

So, Slope = 3

And intercept of the line = 4

For graph,

We need to calculate the value of y and X

Using equation (I)

$y=3X+4$

On X = 0,

$y=4$

On y=0,

$X=\dfrac{-4}{3}$

Hence, The slope and intercept of the line is 3 and 4.

Answer 2

Graph will be a parabola. Slope of the line will be 3.

Explanation:

Given: How could the function y=3x2+4 be plotted on a Cartesian graph to produce a straight line?

Find: What would be the numerical values of the slope and intercept of the line?

Solution:

a) If y = mx + b, then the graph plotted for the equation will be a straight line. If  y = mx^2 + b, then the graph will be a parabola.

b) Now to find the values of slope and intercept, let's assume x = t^2 and use equal increments of t^2 along the x axis, when plotting y versus x.

For t = 0, x = 0.

For t = 1, x = 1.

For t = 1.414, x = 2

For t = 1.732, x = 3 .

For t= 2, x = 4, etc.

The slope of the line you get will be 3.