Question

Given the graph of function y=kx+by=kx+b. a)Find the value of \mathbf{b}b and angle coefficient k in this graph
b) write the function

Answer 1

$k = 1 , \: b = 4 ; \\ y = x + 4.$

Объяснение:

$y = kx + b \\ \text{on \: graph \: we \: can \: see: } \\ y( - 4) = 0; \: y(0) = 4 \\$

If x1 = -4, then y1 = 0

If x2 = 0, then y2 = 4.

Also:

$y(0) = k \times 0 + b = b = y(0)$

$k = \frac{\Delta y}{\Delta x} = \frac{y_2-y_1}{x_2-x_1}$

So:

$b = y(0); \: \: y(0) = 4 \: &= &b = 4 ; \\ k = \frac{y_2-y_1}{x_2-x_1}; \\ k = \frac{4-0}{0-( - 4)} = \frac{4}{4} & = &k = 1 \\$

And function is:

$y = x + 4$