Question

A line passes through the points (4,17) and (7,20). Write a linear function rule in terms of x and y
for this line.
The linear function rule is y=?

Answer 1

Answer:

The linear function rule is $\mathbf{y=x+13}$

Step-by-step explanation:

A line passes through the points (4,17) and (7,20). Write a linear function rule in terms of x and y

for this line.

The function rule is of form: y=mx+b

Where m is slope and b is y-intercept

Finding slope using formula: $Slope=\frac{y_2-y_1}{x_2-x_1}$

We have $x_1=4, y_1=17, x_2=7, y_2=20$

Putting values and finding slope

$Slope=\frac{y_2-y_1}{x_2-x_1}\\Slope=\frac{20-17}{7-4}\\Slope=\frac{3}{3}\\Slope=1$

Finding y-intercept b

Using the point (4,17) to find y-intercept b

$y=mx+b\\17=1(4)+b\\17=4+b\\b=17-4\\b=13$

So, the linear function rule is:

$y=mx+b\\y=1x+13\\\mathbf{y=x+13}$

The linear function rule is $\mathbf{y=x+13}$

Answer 2

A line passes through the points (4,17) and (7,20).

The linear function rule is y= 1x+13

Given :

A line passes through the points (4,17) and (7,20).

The linear function is y=mx+b where m is the slope

lets find out slope using formula

$m=\frac{y_2-y_1}{x_2-x_1} \\(4,17) and (7,20)\\m=\frac{20-17}{7-4}=1$

Slope of the line using the given points is 1

Lets pick any one point (4,17) and use slope to find function rule y

y=mx+b

x is 4  and y is 17  and m=1

$17=1(4)+b\\17=4+b\\17-4=b\\13=b$

Replace the value of 'b' and write the equation

$y=mx+b\\y=1x+13$

The linear function rule is y= 1x+13

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