Question

Write the equation of a line that goes through the points (-5,6) and (10,-6). The final answer should be in Slope Intercept Form

Answer 1

Answer:

$y = -\frac{4}{5}x + 2$

Step-by-step explanation:

Find slope (m) using two points (-5, 6) and (10, -6).

$slope (m) = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-6 - 6}{10 - (-5)} = \frac{-12}{15} = -\frac{4}{5}$

m = -⅘

To find y-intercept (b), substitute x = -5, y = 6, and m = ⅘ into y = mx + b

6 = (-⅘)(-5) + b

6 = 4 + b

6 - 4 = b (subtraction property of equality)

b = 2

To write the equation, substitute m = -⅘, and b = 2 into y = mx + b

The equation of the line would be:

✅$y = -\frac{4}{5}x + 2$

Answer 2

The equation of a line that goes through the points (-5,6) and (10,-6 in slope-intercept form is $y = -\frac 45x + 2$

What is linear equation?

A linear equation is an equation that have a constant rate of change or slope

From the question, we have the following ordered pairs

(x,y) = (-5,6) and (10,-6)

So, the slope (m) is then calculated as:

$m =\frac{y_2 -y_1}{x_2 -x_1}$

This gives

$m =\frac{-6 - 6}{10 + 5}$

Evaluate the differences

$m =-\frac{12}{15}$

Reduce the fraction

$m =-\frac{4}{5}$

The equation is then calculated as:

$y = m(x -x_1) + y_1$

So, we have:

$y = -\frac 45(x + 5) + 6$

Open the bracket

$y = -\frac 45x -4 + 6$

Evaluate the difference

$y = -\frac 45x + 2$

Hence, the equation in slope-intercept form is $y = -\frac 45x + 2$

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