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 [tex]\frac{y_2-y_1}{x_2-x_1}[/tex], where [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] 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
[tex]x_1=16\\y_1=0\\x_2=17\\y_2=12[/tex]
Now let's plug these values into the formula to find the slope
m=[tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
m=[tex]\frac{12-0}{17-16}[/tex]
Subtract
m=[tex]\frac{12}{1}[/tex]
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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