Question

Referring to the figure, write an equation of the line shown in the graph. Use the slope and y-intercept format: y = mx + b (4,5)​

Answer 1

Considering that the line goes through the points (0,1) and (4,5), the equation of the line is:

$y = x + 1$

What is a linear function?

The equation of a line, in slope-intercept form, is given by:

$y = mx + b$

In which:

• m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.

• b is the y-intercept, which is the value of y when x = 0.

In this problem, the line goes through points (0,1) and (4,5). Considering the slope is given by change in y divided by change in x, we have that:

$m = \frac{5 - 1}{4 - 0} = 1$

When x = 0, y = 1, hence the y-intercept is $b = 1$, and the equation is:

$y = x + 1$

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