Question

Write the equation of a line in slope interest form that passes through (16,0) and (17,12)

Answer 1

Answer:

y=12x - 192

Step-by-step explanation:

Hi there!

We are given the points (16,0) and (17, 12)

We want to write the equation of the line that contains these points in slope-intercept form

Slope-intercept form is given as y=mx+b, where m is the slope and b is the y intercept

First, we need to find the slope

The slope (m) can be found using the formula $\frac{y_2-y_1}{x_2-x_1}$, where $(x_1, y_1)$ and $(x_2, y_2)$ are points

We have 2 points, which is what we need to find the slope, but let's label their values to help avoid confusion and mistakes

$x_1=16\\y_1=0\\x_2=17\\y_2=12$

Now let's plug these values into the formula to find the slope

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

m=$\frac{12-0}{17-16}$

Subtract

m=$\frac{12}{1}$

Divide

m = 12

The slope of the line is 12.

Let's substitute that as m in y=mx+b.

Here is our equation so far:

y=12x + b

Now we need to find b

As the equation passes through the points (16,0) and (17, 12), we can use either one of them to solve for b.
Using (16,0) for example:

Substitute 16 as x and 0 as y.

0 = 12(16) + b

Multiply

0 = 192 + b

Subtract 192 from both sides

-192 = b

Substitute -192 as b in the equation

y = 12x - 192

Hope this helps!

Topic: finding the equation of the line

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