Answer:
[tex]y=\frac{7}{2} x -8[/tex]
Step-by-step explanation:
We are given that a line contains these 2 points: (4,6) and (0,-8), in slope-intercept form
Slope-intercept form is given as y=mx+b, where m is the slope and b is the value of y at the y intercept
First, we need to find the slope of the line
The slope can be calculated 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
Even though we have 2 points, let's label their values to avoid any confusion and mistakes when calculating:
[tex]x_1=4\\y_1=6\\x_2=0\\y_2=-8[/tex]
Now substitute into the formula
m=[tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
m=[tex]\frac{-8-6}{0-4}[/tex]
Subtract
m=[tex]\frac{-14}{-4}[/tex]
Divide
m=[tex]\frac{7}{2}[/tex]
The slope is 7/2
Here is the equation of the line so far:
[tex]y=\frac{7}{2}x + b[/tex]
We now need to find b
As the equation passes through (4,6) and (0,-8), we can use either one of them to help solve for b.
Taking (4,6) for instance:
[tex]6=\frac{7}{2}(4) + b[/tex]
Multiply
[tex]6=14 + b[/tex]
Subtract
-8 = b
The equation therefore is:
[tex]y=\frac{7}{2} x -8[/tex]
Topic: slope-intercept form
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