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Sagot :
Answer:
y = 3x - 13
Step-by-step explanation:
We are given the points (7,8) and (3,-4)
We want to write an equation of the line that passes through those 2 points.
There are 3 ways to write the equation of the line:
- Slope-intercept form, which is y=mx+b, where m is the slope and b is the value of y at the y intercept.
- Standard form, which is ax+by=c, where a, b, and c are free integer coefficients, but a and b cannot be 0 and a cannot be negative.
- Point-slope form, which is [tex]y-y_1=m(x-x_1)[/tex], where m is the slope and [tex](x_1 ,y_1)[/tex] is a point.
Although while any one of these options work, the most common way is to use slope-intercept form, so let's do it that way.
First, we need to find the slope of the line.
The slope (m) can be found using this 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 already have 2 points, let's label their values to avoid any confusion.
[tex]x_1=7\\y_1=8\\x_2=3\\y_2=-4[/tex]
Now substitute these values into the formula.
m=[tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
m=[tex]\frac{-4-8}{3-7}[/tex]
Subtract.
m=[tex]\frac{-12}{-4}[/tex]
Divide.
m = 3
The slope of the line is 3.
Here is the equation of the line so far:
y = 3x + b
We now need to find b.
As the equation passes through (7,8) and (3,-4), we can use either one of the points to help us solve for b.
Taking (7,8) for instance:
Substitute 7 as x and 8 as y in the equation.
8 = 3(7) + b
Multiply
8 = 21 + b
Subtract 21 from both sides
-13 = b
Substitute -13 as b in the equation.
y = 3x - 13
Topic: finding the equation of the line
See more: https://brainly.com/question/27951490
A line is a one-dimensional shape that is straight, has no thickness, and extends in both directions indefinitely. The equation of the line that passes through the points (7,8) and (3,-4) is y=3x-13.
What is the equation of a line?
A line is a one-dimensional shape that is straight, has no thickness, and extends in both directions indefinitely. The equation of line is given by,
y =mx + c
where,
x is the coordinate of the x-axis,
y is the coordinate of the y-axis,
m is the slope of the line, and
c is the y-intercept.
The slope of the equation will be,
Slope, m = (-4-8)/(3-7) = -12/-4 = 3
Substitute one of the points in the equation of the line,
-4 = 3(3) + C
C = -13
Hence, the equation of the line that passes through the points (7,8) and (3,-4) is y=3x-13.
Learn more about Equation of Line:
https://brainly.com/question/21511618
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