Question

write the intercept form for each. X Y 0 6 1 10 2 14slope M=y-intercept=b=slope-intercept form

Answer 1

Given the set of values, you have to determine the y-intercept, slope, and the equation that corresponds to de relationship on the table.

The slope-intercept form is

$y=mx+b$

Where

m represents the slope

b represents the y-intercept (is the y-coordinate of the point corresponding to the y-intercept)

The y-intercept of any function in the coordinate system is the point where the line intercepts the y-axis, at this point the x-coordinate is equal to zero. You can determine this value directly from the table, the ordered pair (0,6) corresponds to the y-intercept coordinates.

So "b = 6"

To determine the slope of the line, m, you need to use two points of the line and the following formula:

$m=\frac{y_1-y_2}{x_1-x_2}$

Where

(x₁,y₁) are the coordinates of one point on the line

(x₂,y₂) are the coordinates of a second point on the line

You can use any two points of the line to calculate the slope, I will use (2,14) and (1,10)

$\begin{gathered} m=\frac{14-10}{2-1} \\ m=\frac{4}{1} \\ m=4 \end{gathered}$

The slope of the line is m=4

Finally, you have to replace the values of the slope and y-intercept in the formula to determine the equation of the line in slope-intercept form:

$y=mx+b$

For b=6 and m=4

$y=4x+6$