Question

2. What is the function rule of the line shown?

Answer 1

m = 4/3 , b = -4

f(x)=4/3x-4

First, find m, the slope.

Pick any two points on the line and use this formula: y2-y1/x2-x1

(0,-4) and (3,0)

0-(-4)/3-0 =4/3

So, m=4/3

Now, find b, is the y-intercept (the point on the line the intersects with the y-axis). b=-4

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Answer 2

`\sf m = (4)/(3)`

b = - 4

`\sf f(x) = (4)/(3) x - 4`

Explanation:

let's take two points: (3,0) and (0,-4).

Slope(m):

The slope of a line is a measure of its steepness. It is calculated as the change in y divided by the change in x.

`\sf slope = (y_2 - y_1)/(x_2 - x_1)`

where (x1, y1) and (x2, y2) are two points on the line.

Substituting the coordinates of the points (3,0) and (0,-4) into the slope formula, we get:

`\sf slope (m)= (-4 - 0)/(0 - 3)`

`\sf slope(m)= (4)/(3)`

Equation of the line:

The equation of a line is a mathematical expression that describes the relationship between the x- and y-coordinates of any point on the line.

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

f(x) = mx + b

where m is the slope of the line and b is the y-intercept.

Substituting the slope 4/3 and the coordinates of the point (3,0) into the slope-intercept form, we get:

`\sf 0 = (4)/(3)* 3 + b`

0 = 4 + b

b = -4

Therefore, the equation of the line that passes through the points (3,0) and (0,-4) is:

`\sf f(x) = (4)/(3)* x + (-4)`

`\sf f(x) = (4)/(3) x - 4`

Summary:

`\sf m = (4)/(3)`

b = - 4

`\sf f(x) = (4)/(3) x - 4`