Question

A line passes through the points (2,-4) and (6, 10). What is the equation of the line?​

Answer 1

Answer:

The equation of a line tells us both the y-intercept and the slope of a line on a graph. The equation of a line that passes through the points (2, -4) and (6, 10) is:

$y=\frac{7}{2}x(3.5)-11$

Step-by-step explanation:

• Given:

Two points of the line are (2, -4) and (6, 10).

• To find:

The equation of the line using two ordered pairs (points/coordinates).

The equation of a line with a known/revealed slope (m - variable used) can come in the format of:

y = mx + b

• m = the slope
• b = the y-intercept

Using this information, we can use the formula:

$m=\frac{y_2-y_1}{x_2-x_1}$ (To find the slope/constant of variation/gradient/rate of change) - all synonyms; used for different contexts.

Now using the points, let's plug them into the formula and solve:

$m=\frac{10-(-4)}{6-2}$

$m=\frac{14}{4}$

$m=\frac{7}{2} (\text{Decimal form:} 3.5)$

Now that we have found the slope, let's find the equation of the line.

Let's use the formula: $(y-y_1)=m(x-x_1)$

⇒ Now let's plug in and solve:

       ⇒ $[y-(-4)]=\frac{7}{2} (x-2)$

      ⇒ $y+4=\frac{7}{2} x-7$

   ⇒ $y=\frac{7}{2} x-7-4$

  ⇒ $y=\frac{7}{2} x-11$

Now that we have found the equation of the line, we have completed the question as we have it now answered.

Hence, the equation of the line with the points of (2, -4) and (6,10) is

y = 7/2x - 11

(Keep in mind: This format is known as the slope-intercept form.)

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