Answer :

Given the points of the line:

(2,4) & (-6,-6)

Equation of a line:

y = mx + b;

Where m is the slope and b is the y - intercept.

To find the slope:

[tex]m\text{ =}\frac{y_2-y_1}{x_2-x_1}[/tex][tex]m\text{ = }\frac{-6-4}{-6-2}=\frac{-10}{-8}=\frac{5}{4}[/tex]

To find the y - intercept:

4 = (5/4) x 2 + b

b = 4 - (5/2)

b = 3/2

Equation:

y = 5/4x + 3/2

amysun2025

Answer:

[tex]y = \frac{5}{4} x + \frac{3}{2}[/tex]

Step-by-step explanation:

Pre-Solving

We are given the points (2,4), and (-6, -6).

We want to write the equation of the line using these two points

The equation of the line can be written in three ways:

  •    Slope-intercept form, which is y=mx+b, where m is the slope and b is 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. a is usually non-negative as well.
  •    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.

All three of these forms are valid, however, let's write our equation in slope-intercept form, as that is the most common way to do so.

Solving

Slope

We need to first find the slope of the line.

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.

Let's label the values of our points to avoid any confusion and mistakes.

[tex]x_1=2\\y_1=4\\x_2=-6\\y_2=-6[/tex]

Substitute these values into the formula.

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

[tex]m=\frac{-6-4}{-6-2}[/tex]

Subtract.

[tex]m=\frac{-10}{-8}[/tex]

Simplify

[tex]m=\frac{5}{4}[/tex]

y intercept

We can plug the value of the slope into our equation.

[tex]y=\frac{5}{4} x + b[/tex]

We now need to find the value of b.

As the line passes through (2,4) and (-6, -6), we can use their values to help solve for b.

Either point will work; however, let's take (2,4) as the values are smaller.

Substitute 2 as x and 4 as y.

[tex]4=\frac{5}{4}(2) + b[/tex]

Multiply

[tex]4=\frac{5}{2} + b[/tex]

Subtract 5/2 from both sides.

[tex]4-\frac{5}{2} =b[/tex]

[tex]\frac{3}{2} =b[/tex]

Substitute 3/2 as b.

[tex]y = \frac{5}{4} x + \frac{3}{2}[/tex]

Topic: equation of the line

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